Error correction method and reproduction apparatus

ABSTRACT

A reproduction method includes a step of performing error correction of the first coded data piece and generating error location information which represents an error location of the first coded data; a step of generating erasure locator information which represents an erasure position of the second coded data piece, based on the error location information; and an erasure error correction step of performing erasure error correction of the second coded data piece based on the erasure locator information. The erasure locator information generation step includes the step of, when the error location information indicates that no error is detected in the Nth first symbol and the (N+2)th first symbol and that an error is detected in the (N+1)th first symbol, determining at least one of the plurality of second symbols provided adjacent to the (N+1)th first symbol as representing erasure.

This is a divisional application of co-pending U.S. application Ser. No.10/655,468 filed Sep. 4, 2003.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an error correction method forcorrecting an error of composite coded data having at least one secondsymbol between first symbols forming first coded data which iserror-correction-coded using a first error correction code, betweensynchronization data pieces for synchronizing data, or between the firstsymbol and the synchronization data, the second symbol forming secondcoded data which is error-correction-coded using a second errorcorrection code having a lower degree of redundancy than the first errorcorrection code. The present invention also relates to a reproductionapparatus for carrying out such an error correction method.

2. Description of the Related Art

Optical discs which are representative recording mediums have recentlyincreased in density and capacity, and thus require improvedreliability. Various error correction methods for correcting errorscaused by defects of a recording medium itself or dust or scratches onthe recording medium have been proposed (for example, U.S. Pat. No.6,367,049B1, pages 5 to 6 and FIG. 5; and Japanese National-Phase PCTLaid-Open Publication No. 2001-515642, pages 10 to 11 and FIG. 2).

FIG. 2 shows an exemplary composite coded data piece 203, together witha first coded data piece 201 and a second coded data piece 202. Withreference to FIG. 2, an error correction method will be described.

The composite coded data piece 203 includes first coded data pieces 206,207, 208, 209, 210 and 211 which have been error-correction-coded usinga first error correction code; and second coded data pieces 212, 213,214, 215, 216, 217, 218 and 219 which have been error-correction-codedusing a second error correction code having a lower degree of redundancythan the first error correction code. The composite coded data piece 203also includes synchronization data pieces 204 and 205 for synchronizingthe first coded data piece and the second coded data piece.

The first coded data piece 201 is error-corrected using 24 first errorcorrection codes. The second coded data piece 202 iserror-correction-coded using 304 second error correction codes. Thefirst coded data piece 201 is divided into the plurality of first codeddata pieces 206 through 211. The second coded data piece 202 is dividedinto the plurality of second coded data pieces 212 through 219. Thefirst coded data pieces 206 through 211 each include a plurality offirst symbols, and the second coded data pieces 212 through 219 eachinclude a plurality of second symbols.

Between two adjacent synchronization data pieces, among a plurality ofsynchronization data pieces, at least one first coded data piece isprovided. For example, as shown in FIG. 2, the first coded data pieces206 through 208 including the first symbols are arranged between twoadjacent synchronization data pieces 204 and 205. Thus, at least onefirst symbol is provided between two adjacent synchronization datapieces.

Between the synchronization data piece and the first coded data piece,at least one second coded data piece is provided. Between two adjacentfirst coded data pieces, at least one second coded data piece isprovided. For example, as shown in FIG. 2, the second coded data piece212 is provided between the synchronization data piece 204 and the firstcoded data piece 206. The second coded data piece 213 is providedbetween two adjacent first coded data pieces 206 and 207. Thus, at leastone second symbol is provided between the synchronization data piece andthe first symbol, and between two first symbols. In FIG. 2, 38 secondsymbols are arranged between two first symbols adjacent to each other ina recording direction 220. 38 second symbols are arranged between thesynchronization data piece and the first symbol adjacent to each otherin the recording direction 220.

The first coded data piece 201 and the second coded data piece 202 arerespectively divided into the first coded data pieces 206 through 211and the second coded data pieces 212 through 219 and thus arranged, suchthat local error areas on a recording medium are dispersed in thecomposite coded data piece 203. (Hereinafter, such a process ofarranging the data in a dispersed manner will be referred to as“interleaving”.)

On the recording medium, the above-described composite coded data pieces203 are arranged in the recording direction 220.

The first error correction code is a Reed Solomon code over an extensionfield obtained by adding root α of the primitive polynomial(expression 1) to a prime field GF (2), having 30 information bytes and32 parity bytes. The second error correction code is a Reed Solomon codeover an extension field obtained by adding root α of the primitivepolynomial (expression 1) to a prime field GF(2), having 216 informationbytes and 32 parity bytes.x ⁸ +x ⁴ +x ³ +x ²+1=0  expression 1

FIG. 3 shows a flowchart 30 illustrating an error correction method ofthe composite corrected data piece 203.

In step 301, the first coded data piece 201 is error-corrected. At thispoint, the first coded data piece 201 is subjected to de-interleaving,which is the opposite transform to interleaving.

In step 302, erasure locator information, which indicates a position oferasure in the second coded data piece 202, is generated. The erasurelocator information can be generated by, for example, one of thefollowing three methods.

FIGS. 4 through 6 show the state of the synchronization data pieces orthe first symbols when the second coded data piece is determined torepresent erasure. In FIGS. 4 through 6, mark “X” represents that nosynchronization data piece is detected or that the first symbol isincorrect. Mark “◯” represents that synchronization data is detected orthat the first symbol is correct. FIGS. 4 through 6 show a portion ofthe data corresponding to one row (or a plurality of rows), in therecording direction, of the composite corrected data piece 203 which isarranged in rows and columns.

With reference to FIG. 4, method 1 will be described. When, as shown inFIG. 4, the detection states of both the synchronization data pieces 401and 402 which are adjacent to each other along a recording direction 404(synchronization data pieces 401 and 402 may be first symbols) are “X”,a second coded data piece 403 between the synchronization data pieces401 and 402 is determined to represent erasure. Thus, erasure locatorinformation representing such a determination result is generated.

With reference to FIG. 5, method 2 will be described. When, as shown inFIG. 5, the detection state of the synchronization data pieces 501, 502and 503 which are consecutive in a recording direction 506(synchronization data pieces 501, 502 and 503 may be first symbols) is“X ◯ X”, the second coded data piece 504 between the synchronizationdata pieces 501 and 502, and the second coded data piece 505 between thesynchronization data pieces 502 and 503, are determined to representerasure. Thus, erasure locator information representing such adetermination result is generated.

With reference to FIG. 6, method 3 will be described. When, as shown inFIG. 6, the detection states of three or more consecutive first symbols602 through 604 between synchronization data pieces 601 and 605 whichare adjacent in a recording direction 610 (synchronization data 601 and605 may be first symbols) are “X”, the second coded data pieces 606through 609, including the second coded data piece 606 between the firstsymbol 602 and the synchronization data 601 (detection state: “◯”) andthe second coded data piece 609 between the first symbol 604 and thesynchronization data 605 (detection state: “◯”), are determined torepresent erasure. Thus, erasure locator information representing such adetermination result is generated.

In step 303 (FIG. 3), erasure locator information generated in step 302is used to perform erasure error correction of the second coded datapieces in the range represented by expression 2.ε2ν≦32  expression 2

Here, ε is the number of erasure positions, and ν is the number oferrors other than erasure.

By the above-described methods for generating erasure locatorinformation, a second coded data piece may become undesirablyuncorrectable. FIG. 7 is a partial enlarged view of the compositeencoded data piece 203, which shows an example of an error pattern bywhich the second coded data piece becomes uncorrectable.

Data pieces 701 through 703 are each a first coded data piece or asynchronization data piece. Data pieces 704 through 709 are partial datapieces of the second coded data piece provided in the vicinity of thedata piece 702. At the positions of marks “◯” and “X”, one of a partialsynchronization data piece, a first symbol or a second symbol isprovided. In data pieces 701 through 703, mark “X” represents that nosynchronization data is detected or that the first symbol is incorrect.Mark “◯” represents that synchronization data is detected or that thefirst symbol is correct. In data pieces 704 through 709, mark “X”represents that the second symbol which has been read is incorrect, andthe other portions represent that the second symbol which has been readis correct.

It is assumed that the errors as shown in FIG. 7 occur. By theabove-described methods for generating erasure locator information, thesecond symbols, which are incorrect, are not all determined to representerasure. Since the second coded data is erasure-error-corrected in therange represented by expression 2, only up to 16 errors other thanerasure can be corrected. Therefore, the errors of the pattern as shownin FIG. 7 cannot be corrected.

By the above-mentioned methods for generating erasure locatorinformation, the state determination result of synchronization datapiece which is used for generating the erasure locator information iseither “detected” or “not detected”. When a synchronization data pieceis detected with a positional offset, the symbols positioned before sucha synchronization data piece are incorrect with a high probability, andthe symbols positioned after such a synchronization data piece arecorrect with a high probability. The reason is that the offset of thesynchronization is corrected by a reproduction apparatus, and thesymbols positioned after the synchronization data piece detected with apositional offset is read after the offset of synchronization iscorrected.

In the case where the state determination result of synchronization datapiece is either “detected” or “not detected”, the following occurs. Whena synchronization data piece detected with a positional offset isdetermined to be “detected”, the symbols positioned before such asynchronization data piece may not be determined to represent erasure,despite the fact that these symbols are incorrect. As a result, theincorrect symbols may not be corrected. When a synchronization datapiece detected with a positional offset is determined to be “notdetected”, even the correct symbols positioned after such asynchronization data piece may be determined to represent erasure. Insuch a case, the number of erasure positions is increased and thecorrection may become impossible.

SUMMARY OF THE INVENTION

According to one aspect of the invention, a reproduction method forreproducing a composite coded data piece from a recording medium havingthe composite coded data piece recorded thereon is provided. Thecomposite coded data piece includes a first coded data piece which iserror-correction-coded using a first error correction code, and a secondcoded data piece which is error-correction-coded using a second errorcorrection code having a lower degree of redundancy than that of thefirst error correction code. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one of the plurality of secondsymbols is provided between two adjacent first symbols of the pluralityof first symbols. The plurality of first symbols include an Nth firstsymbol, an (N+1)th first symbol and an (N+2)th first symbol, where N isan integer. The reproduction method includes a reading step of readingthe composite coded data piece from the recording medium and outputtingthe first coded data piece and the second coded data piece; an errorlocation information generation step of performing error correction ofthe first coded data piece and generating error location informationwhich represents an error location of the first coded data; an erasurelocator information generation step of generating erasure locatorinformation which represents an erasure position of the second codeddata piece, based on the error location information; and an erasureerror correction step of performing erasure error correction of thesecond coded data piece based on the erasure locator information. Theerasure locator information generation step includes the step of, whenthe error location information indicates that no error is detected inthe Nth first symbol and the (N+2)th first symbol and that an error isdetected in the (N+1)th first symbol, determining at least one of theplurality of second symbols provided adjacent to the (N+1)th firstsymbol as representing erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of, when the error locationinformation indicates that no error is detected in the Nth first symboland the (N+2)th first symbol and that an error is detected in the(N+1)th first symbol, determining at least one second symbol providedadjacent to the (N+1)th first symbol, among at least one second symbolprovided between the Nth first symbol and the (N+1)th first symbol asrepresenting erasure; and determining at least one second symbolprovided adjacent to the (N+1)th first symbol, among at least one secondsymbol provided between the (N+1)th first symbol and the (N+2)th firstsymbol as representing erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of, when the error locationinformation indicates that an error is detected in both of two adjacentfirst symbols, determining all the second symbols provided between thetwo adjacent first symbols as representing erasure.

According to another aspect of the invention, a reproduction method forreproducing a composite coded data piece from a recording medium havingthe composite coded data piece recorded thereon is provided. Thecomposite coded data piece includes a first coded data piece which iserror-correction-coded using a first error correction code, and secondcoded data piece which is error-correction-coded using a second errorcorrection code having a lower degree of redundancy than that of thefirst error correction code. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least two of the plurality of secondsymbols are provided between two adjacent first symbols of the pluralityof first symbols. The reproduction method includes a reading step ofreading the composite coded data piece from the recording medium andoutputting the first coded data piece and the second coded data piece;an error location information generation step of performing errorcorrection of the first coded data piece and generating error locationinformation which represents an error location of the first coded data;an erasure locator information generation step of generating erasurelocator information which represents an erasure position of the secondcoded data piece, based on the error location information; and anerasure error correction step of performing erasure error correction ofthe second coded data piece based on the erasure locator information.The erasure locator information generation step includes the step of,when the error location information indicates that a first symboldetected to have no error and a first symbol detected to have an errorare adjacent to each other, determining at least one second symbolprovided adjacent to the first symbol detected to have an error, amongat least two second symbols provided between the first symbol detectedto have no error and the first symbol detected to have an error, asrepresenting erasure; and determining at least one second symbolprovided adjacent to the first symbol detected to have no error as notrepresenting erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of, when the error locationinformation indicates that an error is detected in both of two adjacentfirst symbols, determining all the second symbols provided between thetwo adjacent first symbols as representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a coded data piece from a recording medium havinga plurality of synchronization data pieces and the coded data piecewhich is error-correction-coded recorded thereon is provided. The codeddata piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces among the plurality of synchronization data pieces. Theplurality of synchronization data pieces include an Nth synchronizationdata piece, an (N+1)th synchronization data piece, and an (N+2)thsynchronization data piece, where N is an integer. The reproductionmethod includes a reading step of reading the plurality ofsynchronization data pieces and the coded data piece from the recordingmedium; a synchronization detection information generation step ofdetecting states of the plurality of synchronization data pieces andgenerating synchronization detection information which represents thedetection result; an erasure locator information generation step ofgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction step of performing erasureerror correction of the coded data piece based on the erasure locatorinformation. The erasure locator information generation step includesthe step of, when the synchronization detection information indicatesthat the Nth synchronization data piece and the (N+2)th synchronizationdata piece are detected and the (N+1)th synchronization data piece isnot detected, determining at least one of the plurality of symbolsprovided adjacent to the (N+1)th synchronization data piece asrepresenting erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of, when the synchronizationdetection information indicates that the Nth synchronization data pieceand the (N+2)th synchronization data piece are detected and the (N+1)thsynchronization data piece is not detected, determining at least onesymbol provided adjacent to the (N+1)th synchronization data piece,among at least one symbol provided between the Nth synchronization datapiece and the (N+1)th synchronization data piece as representingerasure; and determining at least one symbol provided adjacent to the(N+1)th synchronization data piece, among at least one symbol providedbetween the (N+1)th synchronization data piece and the (N+2)thsynchronization data piece as representing erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of, when the synchronizationdetection information indicates that neither of the two adjacentsynchronization data pieces are detected, determining all the symbolsprovided between the two undetected synchronization data pieces asrepresenting erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a coded data piece from a recording medium havinga plurality of synchronization data pieces and the coded data piecewhich is error-correction-coded recorded thereon is provided. The codeddata piece includes a plurality of symbols. At least two of theplurality of symbols are provided between two adjacent synchronizationdata pieces of the plurality of synchronization data pieces. Thereproduction method includes a reading step of reading the plurality ofsynchronization data pieces and the coded data piece from the recordingmedium; a synchronization detection information generation step ofdetecting states of the plurality of synchronization data pieces andgenerating synchronization detection information which represents thedetection result; an erasure locator information generation step ofgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction step of performing erasureerror correction of the coded data piece based on the erasure locatorinformation. The erasure locator information generation step includesthe step of, when the synchronization detection information indicatesthat a synchronization data piece adjacent to a detected synchronizationdata piece is not detected, determining at least one symbol adjacent tothe undetected synchronization data piece, among at least two symbolsprovided between the detected synchronization data piece and theundetected synchronization data piece, as representing erasure; anddetermining at least one symbol provided adjacent to the detectedsynchronization data piece as not representing erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of, when the synchronizationdetection information indicates that neither of the two adjacentsynchronization data pieces are detected, determining all the symbolsprovided between the two undetected synchronization data pieces asrepresenting erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The reproduction method includes a reading step of readingthe composite coded data piece from the recording medium and outputtingthe first coded data piece, the second coded data piece, and theplurality of synchronization data pieces; a synchronization detectioninformation generation step of detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an error locationinformation generation step of performing error correction of the firstcoded data piece and generating error location information whichrepresents an error location of the first coded data; an erasure locatorinformation generation step of generating erasure locator informationwhich represents an erasure position of the second coded data piece,based on the error location information and the synchronizationdetection information; and an erasure error correction step ofperforming erasure error correction of the second coded data piece basedon the erasure locator information. The erasure locator informationgeneration step includes the step of, when the synchronization detectioninformation indicates that there is a synchronization data piece whichis not detected and the error location information indicates that noerror is detected in the first symbols immediately on both sides of theundetected synchronization data piece, determining at least one of theplurality of second symbols provided adjacent to the undetectedsynchronization data piece as representing erasure.

In one embodiment of the invention, at least two first symbols areprovided between two adjacent synchronization data pieces among theplurality of synchronization data pieces. At least one second symbol isprovided between two adjacent first symbols among the at least two firstsymbols. The erasure locator information generation step furtherincludes the step of, when the error location information indicates thatthere is a first symbol detected to have an error and at least one ofthe error location information and the synchronization detectioninformation indicates that one of a detected synchronization data pieceand a first symbol detected to have no error is immediately on each ofboth sides of the first symbol detected to have an error, determining atleast one of the plurality of second symbols provided adjacent to thefirst symbol detected to have an error as representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a coded data piece from a recording medium havinga plurality of synchronization data pieces and the coded data piecewhich is error-correction-coded recorded thereon is provided. The codeddata piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces among the plurality of synchronization data pieces. Theplurality of synchronization data pieces include an Nth synchronizationdata piece and an (N+1)th synchronization data piece, where N is aninteger. The reproduction method includes a reading step of reading theplurality of synchronization data pieces and the coded data piece fromthe recording medium; a synchronization detection information generationstep of detecting states of the plurality of synchronization data piecesand generating synchronization detection information which representsthe detection result; an erasure locator information generation step ofgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction step of performing erasureerror correction of the coded data piece based on the erasure locatorinformation. The erasure locator information generation step includesthe step of, when the synchronization detection information indicatesthat the (N+1)th synchronization data piece is detected with apositional offset, determining at least one symbol provided between theNth synchronization data piece and the (N+1)th synchronization datapiece as representing erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an (N+2)th synchronization data piece. The erasurelocator information generation step further includes the step of, whenthe synchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one symbol provided between the (N+1)thsynchronization data piece and the (N+2)th synchronization data piece asnot representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The plurality of synchronization data pieces include anNth synchronization data piece and an (N+1)th synchronization datapiece, where N is an integer. The reproduction method includes a readingstep of reading the composite coded data piece from the recording mediumand outputting the first coded data piece, the second coded data piece,and the plurality of synchronization data pieces; a synchronizationdetection information generation step of detecting states of theplurality of synchronization data pieces and generating synchronizationdetection information which represents the detection result; an errorlocation information generation step of performing error correction ofthe first coded data piece and generating error location informationwhich represents an error location of the first coded data; an erasurelocator information generation step of generating erasure locatorinformation which represents an erasure position of the second codeddata piece, based on the error location information and thesynchronization detection information; and an erasure error correctionstep of performing erasure error correction of the second coded datapiece based on the erasure locator information. The erasure locatorinformation generation step includes the step of, when thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one second symbol provided between the Nthsynchronization data piece and the (N+1)th synchronization data piece asrepresenting erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an (N+2)th synchronization data piece. The erasurelocator information generation step further includes the step of, whenthe synchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one second symbol provided between the (N+1)thsynchronization data piece and the (N+2)th synchronization data piece asnot representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The plurality of synchronization data pieces include anNth synchronization data piece and an (N+1)th synchronization datapiece, where N is an integer. A prescribed first symbol is providedbetween the Nth synchronization data piece and the (N+1)thsynchronization data piece. The reproduction method includes a readingstep of reading the composite coded data piece from the recording mediumand outputting the first coded data piece, the second coded data piece,and the plurality of synchronization data pieces; a synchronizationdetection information generation step of detecting states of theplurality of synchronization data pieces and generating synchronizationdetection information which represents the detection result; an errorlocation information generation step of performing error correction ofthe first coded data piece and generating error location informationwhich represents an error location of the first coded data; an erasurelocator information generation step of generating erasure locatorinformation which represents an erasure position of the second codeddata piece, based on the error location information and thesynchronization detection information; and an erasure error correctionstep of performing erasure error correction of the second coded datapiece based on the erasure locator information. The erasure locatorinformation generation step includes the step of, when thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one second symbol provided between the prescribedfirst symbol and the (N+1)th synchronization data piece as representingerasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an (N+2)th synchronization data piece. Anotherprescribed first symbol is provided between the (N+1)th synchronizationdata piece and the (N+2)th synchronization data piece. The erasurelocator information generation step further includes the step of, whenthe synchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one second symbol provided between the (N+1)thsynchronization data piece and the another prescribed first symbol asnot representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a coded data piece from a recording medium havinga plurality of synchronization data pieces and the coded data piecewhich is error-correction-coded recorded thereon is provided. The codeddata piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces of the plurality of synchronization data pieces. Thereproduction method includes a reading step of reading the plurality ofsynchronization data pieces and the coded data piece from the recordingmedium; a synchronization detection information generation step ofdetecting states of the plurality of synchronization data pieces andgenerating synchronization detection information which represents thedetection result; an erasure locator information generation step ofgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction step of performing erasureerror correction of the coded data piece based on the erasure locatorinformation. The erasure locator information generation step includesthe step of, when the synchronization detection information indicatesthat any two or more data pieces from undetected synchronization datapieces and synchronization data pieces detected with a positional offsetare consecutive, determining at least one symbol provided between theconsecutive synchronization data pieces as representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The reproduction method includes a reading step of readingthe composite coded data piece from the recording medium and outputtingthe first coded data piece, the second coded data piece, and theplurality of synchronization data pieces; a synchronization detectioninformation generation step of detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an error locationinformation generation step of performing error correction of the firstcoded data piece and generating error location information whichrepresents an error location of the first coded data; an erasure locatorinformation generation step of generating erasure locator informationwhich represents an erasure position of the second coded data piece,based on the error location information and the synchronizationdetection information; and an erasure error correction step ofperforming erasure error correction of the second coded data piece basedon the erasure locator information. The erasure locator informationgeneration step of, when the synchronization detection informationindicates that any two or more data pieces from undetectedsynchronization data pieces and synchronization data pieces detectedwith a positional offset are consecutive, determining at least onesecond symbol provided between the consecutive synchronization datapieces as representing erasure.

In one embodiment of the invention, the erasure locator informationgeneration step further includes the step of determining at least onefirst symbol provided between the consecutive synchronization datapieces as representing erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, and a second coded data piece which is error-correction-codedusing a second error correction code having a lower degree of redundancythan that of the first error correction code. The first coded data pieceincludes a plurality of first symbols. The second coded data pieceincludes a plurality of second symbols. At least one of the plurality ofsecond symbols is provided between two adjacent first symbols of theplurality of first symbols. The reproduction method includes a readingstep of reading the composite coded data piece from the recording mediumand outputting the first coded data piece and the second coded datapiece; an error location information generation step of performing errorcorrection of the first coded data piece and generating error locationinformation which represents an error location of the first coded data;an erasure locator information generation step of generating at leastfirst erasure locator information and second erasure locator informationwhich represent an erasure position of the second coded data piece,based on the error location information; and an erasure error correctionstep of performing erasure error correction of the second coded datapiece based on at least one of the first erasure locator information andthe second erasure locator information. The erasure error correctionstep includes the step of, when there is an error which cannot becorrected based on the first erasure locator information, performingerasure error correction of the second coded data piece based on thesecond erasure locator information.

In one embodiment of the invention, the erasure locator informationgeneration step includes the steps of: when all the errors can becorrected based on the first erasure locator information, generatingerasure locator information for erasure error correction of anothersecond coded data piece using an identical method as the method used forgenerating the first erasure locator information, and when all theerrors can be corrected based on the second erasure locator information,generating erasure locator information for erasure error correction ofanother second coded data piece using an identical method as the methodused for generating the second erasure locator information.

In one embodiment of the invention, the plurality of first symbolsinclude an Nth first symbol, an (N+1)th first symbol and an (N+2)thfirst symbol, where N is an integer. The erasure locator informationgeneration step includes the step of, when the error locationinformation indicates that no error is detected in the Nth first symboland the (N+2)th first symbol and that an error is detected in the(N+1)th first symbol, determining at least one of the plurality ofsecond symbols provided adjacent to the (N+1)th first symbol asrepresenting erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a coded data piece from a recording medium havinga plurality of synchronization data pieces and the coded data piecewhich is error-correction-coded recorded thereon is provided. The codeddata piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces among the plurality of synchronization data pieces. Thereproduction method includes a reading step of reading the plurality ofsynchronization data pieces and the coded data piece from the recordingmedium; a synchronization detection information generation step ofdetecting states of the plurality of synchronization data pieces andgenerating synchronization detection information which represents thedetection result; an erasure locator information generation step ofgenerating at least first erasure locator information and second erasurelocator information which represent an erasure position of the codeddata piece, based on the synchronization detection information; and anerasure error correction step of performing erasure error correction ofthe coded data piece based on at least one of the first erasure locatorinformation and the second erasure locator information. The erasureerror correction step includes the step of, when there is an error whichcannot be corrected based on the first erasure locator information,performing erasure error correction of the coded data piece based on thesecond erasure locator information.

In one embodiment of the invention, the erasure locator informationgeneration step includes the steps of when all the errors can becorrected based on the first erasure locator information, generatingerasure locator information for erasure error correction of anothercoded data piece using an identical method as the method used forgenerating the first erasure locator information, and when all theerrors can be corrected based on the second erasure locator information,generating erasure locator information for erasure error correction ofanother coded data piece using an identical method as the method usedfor generating the second erasure locator information.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an Nth synchronization data piece, an (N+1)thsynchronization data piece, and an (N+2)th synchronization data piece,where N is an integer. The erasure locator information generation stepincludes the step of, when the synchronization detection informationindicates that the Nth synchronization data piece and the (N+2)thsynchronization data piece are detected and the (N+1)th synchronizationdata piece is not detected, determining at least one of the plurality ofsymbols provided adjacent to the (N+1)th synchronization data piece asrepresenting erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an Nth synchronization data piece and an (N+1)thsynchronization data piece, where N is an integer. The erasure locatorinformation generation step includes the step of, when thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one symbol provided between the Nth synchronizationdata piece and the (N+1)th synchronization data piece as representingerasure.

In one embodiment of the invention, the erasure locator informationgeneration step includes the step of, when the synchronization detectioninformation indicates that any two or more data pieces from undetectedsynchronization data pieces and synchronization data pieces detectedwith a positional offset are consecutive, determining at least onesymbol provided between the consecutive synchronization data pieces asrepresenting erasure.

According to still another aspect of the invention, a reproductionmethod for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The reproduction method includes a reading step of readingthe composite coded data piece from the recording medium and outputtingthe first coded data piece, the second coded data piece, and theplurality of synchronization data pieces; a synchronization detectioninformation generation step of detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an error locationinformation generation step of performing error correction of the firstcoded data piece and generating error location information whichrepresents an error location of the first coded data; an erasure locatorinformation generation step of generating at least first erasure locatorinformation and second erasure locator information which represent anerasure position of the second coded data piece, based on the errorlocation information and the synchronization detection information; andan erasure error correction step of performing erasure error correctionof the second coded data piece based on at least one of the firsterasure locator information and the second erasure locator information.The erasure error correction step includes the step of, when there is anerror which cannot be corrected based on the first erasure locatorinformation, performing erasure error correction of the second codeddata piece based on the second erasure locator information.

In one embodiment of the invention, the erasure locator informationgeneration step includes the steps of: when all the errors can becorrected based on the first erasure locator information, generatingerasure locator information for erasure error correction of anothersecond coded data piece using an identical method as the method used forgenerating the first erasure locator information, and when all theerrors can be corrected based on the second erasure locator information,generating erasure locator information for erasure error correction ofanother second coded data piece using an identical method as the methodused for generating the second erasure locator information.

In one embodiment of the invention, the erasure locator informationgeneration step includes the steps of, when the synchronizationdetection information indicates that there is a synchronization datapiece which is not detected and the error location information indicatesthat no error is detected in the first symbols immediately on both sidesof the undetected synchronization data piece, determining at least oneof the plurality of second symbols provided adjacent to the undetectedsynchronization data piece as representing erasure.

In one embodiment of the invention, at least two first symbols areprovided between two adjacent synchronization data pieces among theplurality of synchronization data pieces. At least one second symbol isprovided between two adjacent first symbols among the at least two firstsymbols. The erasure locator information generation step includes thestep of, when the error location information indicates that there is afirst symbol detected to have an error and at least one of the errorlocation information and the synchronization detection informationindicates that one of a detected synchronization data piece and a firstsymbol detected to have no error is immediately on each of both sides ofthe first symbol detected to have an error, determining at least one ofthe plurality of second symbols provided adjacent to the first symboldetected to have an error as representing erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an Nth synchronization data piece and an (N+1)thsynchronization data piece, where N is an integer. The erasure locatorinformation generation step includes the step of, when thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one second symbol provided between the Nthsynchronization data piece and the (N+1)th synchronization data piece asrepresenting erasure.

In one embodiment of the invention, the erasure locator informationgeneration step includes the step of, when the synchronization detectioninformation indicates that any two or more data pieces from undetectedsynchronization data pieces and synchronization data pieces detectedwith a positional offset are consecutive, determining at least onesecond symbol provided between the consecutive synchronization datapieces as representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, and a second coded data piece which is error-correction-codedusing a second error correction code having a lower degree of redundancythan that of the first error correction code. The first coded data pieceincludes a plurality of first symbols. The second coded data pieceincludes a plurality of second symbols. At least one of the plurality ofsecond symbols is provided between two adjacent first symbols of theplurality of first symbols. The plurality of first symbols include anNth first symbol, an (N+1)th first symbol and an (N+2)th first symbol,where N is an integer. The reproduction apparatus includes a readingsection for reading the composite coded data piece from the recordingmedium and outputting the first coded data piece and the second codeddata piece; an error location information generation section forperforming error correction of the first coded data piece and generatingerror location information which represents an error location of thefirst coded data; an erasure locator information generation section forgenerating erasure locator information which represents an erasureposition of the second coded data piece, based on the error locationinformation; and an erasure error correction section for performingerasure error correction of the second coded data piece based on theerasure locator information. When the error location informationindicates that no error is detected in the Nth first symbol and the(N+2)th first symbol and that an error is detected in the (N+1)th firstsymbol, the erasure locator information generation section determines atleast one of the plurality of second symbols provided adjacent to the(N+1)th first symbol as representing erasure.

In one embodiment of the invention, when the error location informationindicates that no error is detected in the Nth first symbol and the(N+2)th first symbol and that an error is detected in the (N+1)th firstsymbol, the erasure locator information generation section determines atleast one second symbol provided adjacent to the (N+1)th first symbol,among at least one second symbol provided between the Nth first symboland the (N+1)th first symbol as representing erasure; and determining atleast one second symbol provided adjacent to the (N+1)th first symbol,among at least one second symbol provided between the (N+1)th firstsymbol and the (N+2)th first symbol as representing erasure.

In one embodiment of the invention, when the error location informationindicates that an error is detected in both of two adjacent firstsymbols, the erasure locator information generation section determinesall the second symbols provided between the two adjacent first symbolsas representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, and a second coded data piece which is error-correction-codedusing a second error correction code having a lower degree of redundancythan that of the first error correction code. The first coded data pieceincludes a plurality of first symbols. The second coded data pieceincludes a plurality of second symbols. At least two of the plurality ofsecond symbols are provided between two adjacent first symbols of theplurality of first symbols. The reproduction apparatus includes areading section for reading the composite coded data piece from therecording medium and outputting the first coded data piece and thesecond coded data piece; an error location information generationsection for performing error correction of the first coded data pieceand generating error location information which represents an errorlocation of the first coded data; an erasure locator informationgeneration section for generating erasure locator information whichrepresents an erasure position of the second coded data piece, based onthe error location information; and an erasure error correction sectionfor performing erasure error correction of the second coded data piecebased on the erasure locator information. When the error locationinformation indicates that a first symbol detected to have no error anda first symbol detected to have an error are adjacent to each other, theerasure locator information generation section determines at least onesecond symbol provided adjacent to the first symbol detected to have anerror, among at least two second symbols provided between the firstsymbol detected to have no error and the first symbol detected to havean error, as representing erasure; and determines at least one secondsymbol provided adjacent to the first symbol detected to have no erroras not representing erasure.

In one embodiment of the invention, when the error location informationindicates that an error is detected in both of two adjacent firstsymbols, the erasure locator information generation section determinesall the second symbols provided between the two adjacent first symbolsas representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon is provided. Thecoded data piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces among the plurality of synchronization data pieces. Theplurality of synchronization data pieces include an Nth synchronizationdata piece, an (N+1)th synchronization data piece, and an (N+2)thsynchronization data piece, where N is an integer. The reproductionapparatus includes a reading section for reading the plurality ofsynchronization data pieces and the coded data piece from the recordingmedium; a synchronization detection information generation section fordetecting states of the plurality of synchronization data pieces andgenerating synchronization detection information which represents thedetection result; an erasure locator information generation section forgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction section for performingerasure error correction of the coded data piece based on the erasurelocator information. When the synchronization detection informationindicates that the Nth synchronization data piece and the (N+2)thsynchronization data piece are detected and the (N+1)th synchronizationdata piece is not detected, the erasure locator information generationsection determines at least one of the plurality of symbols providedadjacent to the (N+1)th synchronization data piece as representingerasure.

In one embodiment of the invention, when the synchronization detectioninformation indicates that the Nth synchronization data piece and the(N+2)th synchronization data piece are detected and the (N+1)thsynchronization data piece is not detected, the erasure locatorinformation generation section determines at least one symbol providedadjacent to the (N+1)th synchronization data piece, among at least onesymbol provided between the Nth synchronization data piece and the(N+1)th synchronization data piece as representing erasure; anddetermines at least one symbol provided adjacent to the (N+1)thsynchronization data piece, among at least one symbol provided betweenthe (N+1)th synchronization data piece and the (N+2)th synchronizationdata piece as representing erasure.

In one embodiment of the invention, when the synchronization detectioninformation indicates that neither of the two adjacent synchronizationdata pieces are detected, the erasure locator information generationsection determines all the symbols provided between the two undetectedsynchronization data pieces as representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon is provided. Thecoded data piece includes a plurality of symbols. At least two of theplurality of symbols are provided between two adjacent synchronizationdata pieces of the plurality of synchronization data pieces. Thereproduction apparatus includes a reading section for reading theplurality of synchronization data pieces and the coded data piece fromthe recording medium; a synchronization detection information generationsection for detecting states of the plurality of synchronization datapieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration section for generating erasure locator information whichrepresents an erasure position of the coded data piece, based on thesynchronization detection information; and an erasure error correctionsection for performing erasure error correction of the coded data piecebased on the erasure locator information. When the synchronizationdetection information indicates that a synchronization data pieceadjacent to a detected synchronization data piece is not detected, theerasure locator information generation section determines at least onesymbol provided adjacent to the undetected synchronization data piece,among at least two symbols provided between the detected synchronizationdata piece and the undetected synchronization data piece, asrepresenting erasure; and determines at least one symbol providedadjacent to the detected synchronization data piece as not representingerasure.

In one embodiment of the invention, when the synchronization detectioninformation indicates that neither of the two adjacent synchronizationdata pieces are detected, the erasure locator information generationsection determines all the symbols provided between the two undetectedsynchronization data pieces as representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The reproduction apparatus includes a reading section forreading the composite coded data piece from the recording medium andoutputting the first coded data piece, the second coded data piece, andthe plurality of synchronization data pieces; a synchronizationdetection information generation section for detecting states of theplurality of synchronization data pieces and generating synchronizationdetection information which represents the detection result; an errorlocation information generation section for performing error correctionof the first coded data piece and generating error location informationwhich represents an error location of the first coded data; an erasurelocator information generation section for generating erasure locatorinformation which represents an erasure position of the second codeddata piece, based on the error location information and thesynchronization detection information; and an erasure error correctionsection for performing erasure error correction of the second coded datapiece based on the erasure locator information. When the synchronizationdetection information indicates that there is a synchronization datapiece which is not detected and the error location information indicatesthat no error is detected in the first symbols immediately on both sidesof the undetected synchronization data piece, the erasure locatorinformation generation section determines at least one of the pluralityof second symbols provided adjacent to the undetected synchronizationdata piece as representing erasure.

In one embodiment of the invention, at least two first symbols areprovided between two adjacent synchronization data pieces among theplurality of synchronization data pieces. At least one second symbol isprovided between two adjacent first symbols among the at least two firstsymbols. When the error location information indicates that there is afirst symbol detected to have an error and at least one of the errorlocation information and the synchronization detection informationindicates that one of a detected synchronization data piece and a firstsymbol detected to have no error is immediately on each of both sides ofthe first symbol detected to have an error, the erasure locatorinformation generation section determines at least one of the pluralityof second symbols provided adjacent to the first symbol detected to havean error as representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon is provided. Thecoded data piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces among the plurality of synchronization data pieces. Theplurality of synchronization data pieces include an Nth synchronizationdata piece and an (N+1)th synchronization data piece, where N is aninteger. The reproduction apparatus includes a reading section forreading the plurality of synchronization data pieces and the coded datapiece from the recording medium; a synchronization detection informationgeneration section for detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an erasure locatorinformation generation section for generating erasure locatorinformation which represents an erasure position of the coded datapiece, based on the synchronization detection information; and anerasure error correction section for performing erasure error correctionof the coded data piece based on the erasure locator information. Whenthe synchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset, theerasure locator information generation section determines at least onesymbol provided between the Nth synchronization data piece and the(N+1)th synchronization data piece as representing erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an (N+2)th synchronization data piece. When thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset, theerasure locator information generation section determines at least onesymbol provided between the (N+1)th synchronization data piece and the(N+2)th synchronization data piece as not representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The plurality of synchronization data pieces include anNth synchronization data piece and an (N+1)th synchronization datapiece, where N is an integer. The reproduction apparatus includes areading section for reading the composite coded data piece from therecording medium and outputting the first coded data piece, the secondcoded data piece, and the plurality of synchronization data pieces; asynchronization detection information generation section for detectingstates of the plurality of synchronization data pieces and generatingsynchronization detection information which represents the detectionresult; an error location information generation section for performingerror correction of the first coded data piece and generating errorlocation information which represents an error location of the firstcoded data; an erasure locator information generation section forgenerating erasure locator information which represents an erasureposition of the second coded data piece, based on the error locationinformation and the synchronization detection information; and anerasure error correction section for performing erasure error correctionof the second coded data piece based on the erasure locator information.When the synchronization detection information indicates that the(N+1)th synchronization data piece is detected with a positional offset,the erasure locator information generation section determines at leastone second symbol provided between the Nth synchronization data pieceand the (N+1)th synchronization data piece as representing erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an (N+2)th synchronization data piece. When thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset, theerasure locator information generation section determines at least onesecond symbol provided between the (N+1)th synchronization data pieceand the (N+2)th synchronization data piece as not representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The plurality of synchronization data pieces include anNth synchronization data piece and an (N+1)th synchronization datapiece, where N is an integer. A prescribed first symbol is providedbetween the Nth synchronization data piece and the (N+1)thsynchronization data piece. The reproduction apparatus includes areading section for reading the composite coded data piece from therecording medium and outputting the first coded data piece, the secondcoded data piece, and the plurality of synchronization data pieces; asynchronization detection information generation section for detectingstates of the plurality of synchronization data pieces and generatingsynchronization detection information which represents the detectionresult; an error location information generation section for performingerror correction of the first coded data piece and generating errorlocation information which represents an error location of the firstcoded data; an erasure locator information generation section forgenerating erasure locator information which represents an erasureposition of the second coded data piece, based on the error locationinformation and the synchronization detection information; and anerasure error correction section for performing erasure error correctionof the second coded data piece based on the erasure locator information.When the synchronization detection information indicates that the(N+1)th synchronization data piece is detected with a positional offset,the erasure locator information generation section determines at leastone second symbol provided between the prescribed first symbol and the(N+1)th synchronization data piece as representing erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an (N+2)th synchronization data piece. Anotherprescribed first symbol is provided between the (N+1)th synchronizationdata piece and the (N+2)th synchronization data piece. When thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset, theerasure locator information generation section determines at least onesecond symbol provided between the (N+1)th synchronization data pieceand the another prescribed first symbol as not representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon is provided. Thecoded data piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces of the plurality of synchronization data pieces. Thereproduction apparatus includes a reading section for reading theplurality of synchronization data pieces and the coded data piece fromthe recording medium; a synchronization detection information generationsection for detecting states of the plurality of synchronization datapieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration section for generating erasure locator information whichrepresents an erasure position of the coded data piece, based on thesynchronization detection information; and an erasure error correctionsection for performing erasure error correction of the coded data piecebased on the erasure locator information. When the synchronizationdetection information indicates that any two or more data pieces fromundetected synchronization data pieces and synchronization data piecesdetected with a positional offset are consecutive, the erasure locatorinformation generation section determines at least one symbol providedbetween the consecutive synchronization data pieces as representingerasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The reproduction apparatus includes a reading section forreading the composite coded data piece from the recording medium andoutputting the first coded data piece, the second coded data piece, andthe plurality of synchronization data pieces; a synchronizationdetection information generation section for detecting states of theplurality of synchronization data pieces and generating synchronizationdetection information which represents the detection result; an errorlocation information generation section for performing error correctionof the first coded data piece and generating error location informationwhich represents an error location of the first coded data; an erasurelocator information generation section for generating erasure locatorinformation which represents an erasure position of the second codeddata piece, based on the error location information and thesynchronization detection information; and an erasure error correctionsection for performing erasure error correction of the second coded datapiece based on the erasure locator information. When the synchronizationdetection information indicates that any two or more data pieces fromundetected synchronization data pieces and synchronization data piecesdetected with a positional offset are consecutive, the erasure locatorinformation generation section determines at least one second symbolprovided between the consecutive synchronization data pieces asrepresenting erasure.

In one embodiment of the invention, the erasure locator informationgeneration section determines at least one first symbol provided betweenthe consecutive synchronization data pieces as representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, and a second coded data piece which is error-correction-codedusing a second error correction code having a lower degree of redundancythan that of the first error correction code. The first coded data pieceincludes a plurality of first symbols. The second coded data pieceincludes a plurality of second symbols. At least one of the plurality ofsecond symbols is provided between two adjacent first symbols of theplurality of first symbols. The reproduction apparatus includes areading section for reading the composite coded data piece from therecording medium and outputting the first coded data piece and thesecond coded data piece; an error location information generationsection for performing error correction of the first coded data pieceand generating error location information which represents an errorlocation of the first coded data; an erasure locator informationgeneration section for generating at least first erasure locatorinformation and second erasure locator information which represent anerasure position of the second coded data piece, based on the errorlocation information; and an erasure error correction section forperforming erasure error correction of the second coded data piece basedon at least one of the first erasure locator information and the seconderasure locator information. When there is an error which cannot becorrected based on the first erasure locator information, the erasureerror correction section performs erasure error correction of the secondcoded data piece based on the second erasure locator information.

In one embodiment of the invention, when all the errors can be correctedbased on the first erasure locator information, the erasure locatorinformation generation section generates erasure locator information forerasure error correction of another second coded data piece using anidentical method as the method used for generating the first erasurelocator information. When all the errors can be corrected based on thesecond erasure locator information, the erasure locator informationgeneration section generates erasure locator information for erasureerror correction of another second coded data piece using an identicalmethod as the method used for generating the second erasure locatorinformation.

In one embodiment of the invention, the plurality of first symbolsinclude an Nth first symbol, an (N+1)th first symbol and an (N+2)thfirst symbol, where N is an integer. When the error location informationindicates that no error is detected in the Nth first symbol and the(N+2)th first symbol and that an error is detected in the (N+1)th firstsymbol, the erasure locator information generation section determines atleast one of the plurality of second symbols provided adjacent to the(N+1)th first symbol as representing erasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon is provided. Thecoded data piece includes a plurality of symbols. At least one of theplurality of symbols is provided between two adjacent synchronizationdata pieces among the plurality of synchronization data pieces. Thereproduction apparatus includes a reading section for reading theplurality of synchronization data pieces and the coded data piece fromthe recording medium; a synchronization detection information generationsection for detecting states of the plurality of synchronization datapieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration section for generating at least first erasure locatorinformation and second erasure locator information which represent anerasure position of the coded data piece, based on the synchronizationdetection information; and an erasure error correction section forperforming erasure error correction of the coded data piece based on atleast one of the first erasure locator information and the seconderasure locator information. When there is an error which cannot becorrected based on the first erasure locator information, the erasureerror correction section performs erasure error correction of the codeddata piece based on the second erasure locator information.

In one embodiment of the invention, when all the errors can be correctedbased on the first erasure locator information, the erasure locatorinformation generation section generates erasure locator information forerasure error correction of another coded data piece using an identicalmethod as the method used for generating the first erasure locatorinformation. When all the errors can be corrected based on the seconderasure locator information, the erasure locator information generationsection generates erasure locator information for erasure errorcorrection of another coded data piece using an identical method as themethod used for generating the second erasure locator information.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an Nth synchronization data piece, an (N+1)thsynchronization data piece, and an (N+2)th synchronization data piece,where N is an integer. When the synchronization detection informationindicates that the Nth synchronization data piece and the (N+2)thsynchronization data piece are detected and the (N+1)th synchronizationdata piece is not detected, the erasure locator information generationsection determines at least one of the plurality of symbols providedadjacent to the (N+1)th synchronization data piece as representingerasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an Nth synchronization data piece and an (N+1)thsynchronization data piece, where N is an integer. When thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset, theerasure locator information generation section determines at least onesymbol provided between the Nth synchronization data piece and the(N+1)th synchronization data piece as representing erasure.

In one embodiment of the invention, when the synchronization detectioninformation indicates that any two or more data pieces from undetectedsynchronization data pieces and synchronization data pieces detectedwith a positional offset are consecutive, the erasure locatorinformation generation section determines at least one symbol providedbetween the consecutive synchronization data pieces as representingerasure.

According to still another aspect of the invention, a reproductionapparatus for reproducing a composite coded data piece from a recordingmedium having the composite coded data piece recorded thereon isprovided. The composite coded data piece includes a first coded datapiece which is error-correction-coded using a first error correctioncode, a second coded data piece which is error-correction-coded using asecond error correction code having a lower degree of redundancy thanthat of the first error correction code, and a plurality ofsynchronization data pieces. The first coded data piece includes aplurality of first symbols. The second coded data piece includes aplurality of second symbols. At least one first symbol is providedbetween two adjacent synchronization data pieces among the plurality ofsynchronization data pieces. At least one of the plurality of secondsymbols is provided at least between a synchronization data piece and afirst symbol. The reproduction apparatus includes a reading section forreading the composite coded data piece from the recording medium andoutputting the first coded data piece, the second coded data piece, andthe plurality of synchronization data pieces; a synchronizationdetection information generation section for detecting states of theplurality of synchronization data pieces and generating synchronizationdetection information which represents the detection result; an errorlocation information generation section for performing error correctionof the first coded data piece and generating error location informationwhich represents an error location of the first coded data; an erasurelocator information generation section for generating at least firsterasure locator information and second erasure locator information whichrepresent an erasure position of the second coded data piece, based onthe error location information and the synchronization detectioninformation; and an erasure error correction section for performingerasure error correction of the second coded data piece based on atleast one of the first erasure locator information and the seconderasure locator information. When there is an error which cannot becorrected based on the first erasure locator information, the erasureerror correction section performs erasure error correction of the secondcoded data piece based on the second erasure locator information.

In one embodiment of the invention, when all the errors can be correctedbased on the first erasure locator information, the erasure locatorinformation generation section generates erasure locator information forerasure error correction of another second coded data piece using anidentical method as the method used for generating the first erasurelocator information. When all the errors can be corrected based on thesecond erasure locator information, the erasure locator informationgeneration section generates erasure locator information for erasureerror correction of another second coded data piece using an identicalmethod as the method used for generating the second erasure locatorinformation.

In one embodiment of the invention, when the synchronization detectioninformation indicates that there is a synchronization data piece whichis not detected and the error location information indicates that noerror is detected in the first symbols immediately on both sides of theundetected synchronization data piece, the erasure locator informationgeneration section determines at least one of the plurality of secondsymbols provided adjacent to the undetected synchronization data pieceas representing erasure.

In one embodiment of the invention, at least two first symbols areprovided between two adjacent synchronization data pieces among theplurality of synchronization data pieces. At least one second symbol isprovided between two adjacent first symbols among the at least two firstsymbols. When the error location information indicates that there is afirst symbol detected to have an error and at least one of the errorlocation information and the synchronization detection informationindicates that one of a detected synchronization data piece and a firstsymbol detected to have no error is immediately on each of both sides ofthe first symbol detected to have an error, the erasure locatorinformation generation section determines at least one of the pluralityof second symbols provided adjacent to the first symbol detected to havean error as representing erasure.

In one embodiment of the invention, the plurality of synchronizationdata pieces include an Nth synchronization data piece and an (N+1)thsynchronization data piece, where N is an integer. When thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset, theerasure locator information generation section determines at least onesecond symbol provided between the Nth synchronization data piece andthe (N+1)th synchronization data piece as representing erasure.

In one embodiment of the invention, when the synchronization detectioninformation indicates that any two or more data pieces from undetectedsynchronization data pieces and synchronization data pieces detectedwith a positional offset are consecutive, the erasure locatorinformation generation section determines at least one second symbolprovided between the consecutive synchronization data pieces asrepresenting erasure.

An error correction method and a reproduction apparatus according to thepresent invention function as follows. When a first symbol included in afirst coded data piece having a relatively high degree of redundancy isdetected to have an error or when no synchronization data piece isdetected, the second symbols which are provided in the vicinity of sucha first symbol or the undetected synchronization data piece have a highprobability of incorrect and thus are determined to represent erasure.When a synchronization data piece is detected with a positional offset,symbols included in the coded data pieces located before such asynchronization data piece have a high probability of being incorrectand thus is determined to represent erasure. Symbols included in thecoded data pieces located after such a synchronization data piece have ahigh probability of being correct and thus is determined not torepresent erasure. When at least two of the undetected synchronizationdata pieces and synchronization data pieces detected with a positionaloffset are consecutive, data pieces which are read before the nextcorrectly detected synchronization data piece have a high probability ofbeing incorrect. Thus, symbols included in all the coded data piecesbetween those consecutive synchronization data pieces are determined torepresent erasure. Owing to these methods, erasure positions can bedetermined with higher precision, and thus the error correctioncapability can be improved.

An error correction method and a reproduction apparatus according to thepresent invention are useful for, for example, error correction ofcomposite coded data.

Thus, the invention described herein makes possible the advantages ofproviding an error correction method which is effective for generatingerasure locator information using a result of error correction of afirst coded data piece or a result of detection of a synchronizationdata piece and for performing erasure error correction of a second codeddata piece using the erasure locator information, and a reproductionapparatus for carrying out such an error correction method.

These and other advantages of the present invention will become apparentto those skilled in the art upon reading and understanding the followingdetailed description with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart illustrating an error correction method of acomposite coded data piece according to a first example of the presentinvention;

FIG. 2 shows a structure of a composite coded data piece;

FIG. 3 is a flowchart illustrating an error correction method of acomposite coded data piece;

FIG. 4 shows a state of a synchronization data piece or a first symbolwhen a second coded data piece is determined to represent erasure in theerror correction method;

FIG. 5 shows another state of the synchronization data piece or thefirst symbol when the second coded data piece is determined to representerasure in the error correction method;

FIG. 6 shows still another state of the synchronization data piece orthe first symbol when the second coded data piece is determined torepresent erasure in the error correction method;

FIG. 7 shows an exemplary pattern of errors of the composite coded datapiece;

FIG. 8 is a flowchart of a method for correcting an error of the firstcoded data piece and generating error location information according tothe first example of the present invention;

FIG. 9 shows a state of a synchronization data piece of a first symbolin the first example;

FIG. 10 shows another state of the synchronization data piece of thefirst symbol in the first example;

FIG. 11 shows still another state of the synchronization data piece ofthe first symbol in the first example;

FIG. 12 is a flowchart of a method for correcting an erasure error of asecond coded data piece according to the first example;

FIG. 13 is a flowchart illustrating an error correction method of acomposite coded data piece according to a second example of the presentinvention; and

FIG. 14 shows an exemplary structure of an information reproductionapparatus according to a third example of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, the present invention will be described by way ofillustrative examples with reference to the accompanying drawings.

Example 1

An error correction method according to a first example of the presentinvention will be described. In the following description, the compositecoded data piece 203 shown in FIG. 2 will be used as an example of thecomposite coded data piece.

FIG. 1 is a flowchart 10 illustrating an error correction method of thecomposite coded data piece 203 in this example.

In step 101, the states of the synchronization data pieces 204 and 205are detected in the order of data pieces which have been recorded. Thus,synchronization detection information representing the detection resultis generated. When, for example, a synchronization data piece isdetected, the synchronization detection information associated with thatsynchronization data piece indicates “0”. When no synchronization datapiece is detected, the synchronization detection information associatedwith that synchronization data piece indicates “1”. When asynchronization data piece is detected with a positional offset, thesynchronization detection information associated with thatsynchronization data piece indicates “2”.

In step 102, the first coded data piece 201 is error-corrected. In step103, error location information representing the position of an error ofthe first coded data piece 201 is generated. Since the first coded datapiece 201 is positioned after being interleaved, the error correction isperformed on a first coded data piece 201 which has been de-interleaved.As described above, de-interleaving is the opposite transform tointerleaving. In this manner, the first coded data pieces 206 through211 are error-corrected. This will be described in detail below.

In step 104, erasure locator information representing the position oferasure of the second coded data piece 202 is generated using thesynchronization detection information and the error location informationgenerated in steps 101 and 103. This will be described in detail below.

In step 105, the second coded data piece 202 is erasure-error-correctedusing the erasure locator information generated in step 104.

FIG. 8 is a flowchart 80 illustrating an exemplary method for correctingthe error of the first coded data piece 201 and generating errorlocation information as performed in steps 102 and 103 in FIG. 1.

In step 801, a syndrome representing position information for specifyinga position of an error is calculated. A data piece R to beerror-corrected is:R=(A[0]A[1] . . . A[60]A[61])  expression 3

In this expression, A[i] (i=0 through 61) represents 1 byte, whichcorresponds to 8 bits. Here, the data size of one symbol is 1 byte. A[0]through A[29] represent a data portion, and A[30] through A[61]represent a parity portion. Syndrome S_(j) is defined as:S _(j) =R(α^(j))=A[0]α^(61j) +A[1]α^(60j) + . . . +A[60]α^(j)+A[61]  expression 4

Here, j=0 through 31.

In step 802, it is determined whether syndrome S_(j) is 0 or not. Whensyndrome S_(j) is 0, the processing advances to step 810. In step 810,it is determined that all the symbols A[i] (i=0 through 61) included inthe data piece R are correct. In step 813, error location informationrepresenting “0” regarding all the symbols A[i] (i=0 through 61) isgenerated. When syndrome S_(j) is not 0 in step 802, the processingadvances to step 803.

In step 803, an error locator polynomial is formulated using syndromeS_(j). The error locator polynomial has, as a root, the reciprocalnumber of error locations L1, L2, Lm (m is the number of errors) and isexpressed by: $\begin{matrix}\begin{matrix}{{\alpha(x)} = {( {1 - {\alpha^{L\quad 1}x}} )( {1 - {\alpha^{L\quad 2}x}} )\quad\ldots\quad( {1 - \alpha^{Lm}} )}} \\{= {{\sigma_{m}x^{m}} + {\sigma_{m - 1}x^{m - 1}} + \ldots + {\sigma_{1}x} + 1}}\end{matrix} & {{expression}\quad 5}\end{matrix}$

Each coefficient of the error locator polynomial is defined by syndromeS_(j). The coefficient of the error locator polynomial is found usingPeterson's method, the Euclidean method, or an algorithm such as the BMmethod. Peterson's method solves the simultaneous equations realizedbetween the coefficient of the error locator polynomial and syndromeS_(j), using a matrix. The Euclidean method is a sequential calculationmethod of solving such simultaneous equations using a polynomial.

When the coefficient of the error locator polynomial is found in step804, the processing advances to step 805. When the coefficient is notfound, the processing advances to step 809. In step 809, it isdetermined that a larger number of errors than can be corrected aregenerated. In step 812, error location information representing “1”regarding all the symbols A[i] (i=0 through 61) is generated.

In step 805, α to the -ith power (i=0 through 61, and α is the root ofthe primitive polynomial (expression 1)) is substituted into the errorlocator polynomial. Thus, the value of “k”, at which the solution of theerror locator polynomial is 0, is found. In this way, the position ofthe incorrect data piece (i.e., the error location) is found. The symbolcorresponding to the error location is represented as:A[61-k]  expression 6.

In step 806, it is determined whether or not a calculation for findingthe error location can be performed. When it is determined that thecalculation can be performed in step 806, the processing advances tostep 807. When it is determined that the calculation cannot be performedin step 806, error location information representing “1” regarding allthe symbols A[i] (i=0 through 61) is generated.

In step 807, an error value is calculated by solving the simultaneousequations between the error location found in steps 805 and 806 andsyndrome S_(j).

In step 808, symbol A[61-k] is error-corrected by subtracting the errorvalue obtained in step 807 from the value represented by symbol A[61-k]corresponding to the error location found in steps 805 and 806. In step811, error location information representing “1” regarding symbolA[61-k] is generated. By performing such error correction and generationof error location information, the first coded data piece 201 iserror-corrected.

Hereinafter, a method for generating erasure locator information in step104 in FIG. 1 will be described in detail. Extinction positioninformation is generated by reading and using synchronization detectioninformation of synchronization data pieces positioned before and afterthe second coded data piece for which erasure locator information is tobe generated, and/or error location information of first coded datapieces positioned before and after the second coded data piece for whicherasure locator information is to be generated. In this example, amethod for generating erasure locator information in the case where thesynchronization data pieces and the first symbols are in the state shownin FIGS. 9 through 11. FIGS. 9 through 11 show a portion of the datacorresponding to one row (or a plurality of rows), in a recordingdirection, of the composite corrected data piece 203 which is arrangedin rows and columns.

In FIG. 9, mark “X” indicates a synchronization data piece, thesynchronization detection information of which represents “1”, or afirst symbol, the error location information of which represents “1”.Mark “◯” indicates a synchronization data piece, the synchronizationdetection information of which represents “0”, or a first symbol, theerror location information of which represents “0”.

In one embodiment, an Nth first symbol 901, an (N+1)th first symbol 902,and an (N+2)th first symbol 903 are arranged in a recording direction908. Here, “N” is an integer. It is assumed that no error is detected inthe Nth first symbol 901 and the (N+2)th first symbol 903 but an erroris detected in the (N+1)th first symbol 902. In this case, at least oneof a plurality of second symbols provided immediately on both sides ofthe (N+1)th first symbol 902 is determined to represent erasure. Thus,erasure locator information representing such a determination result isgenerated.

As shown in FIG. 9, a second coded data piece 909 is arranged betweenthe Nth first symbol 901 and the (N+1)th first symbol 902. The secondcoded data piece 909 is divided into two portions, i.e., partial secondcoded data pieces 904 and 906 in accordance with the number of secondsymbols which are determined to represent erasure. The partial secondcoded data pieces 904 and 906 each include at least one second symbol.For generating erasure locator information, at least one second symbolincluded in the partial second coded data piece 904 provided adjacent tothe (N+1)th first symbol 902 is determined to represent erasure. Atleast one second symbol included in the partial second coded data piece906 provided adjacent to the Nth first symbol 901 is determined not torepresent erasure.

A second coded data piece 910 is arranged between the (N+1)th firstsymbol 902 and the (N+2)th first symbol 903. The second coded data piece910 is divided into two portions, i.e., partial second coded data pieces905 and 907 in accordance with the number of second symbols which aredetermined to represent erasure. The partial second coded data pieces905 and 907 each include at least one second symbol. For generatingerasure locator information, at least one second symbol included in thepartial second coded data piece 905 provided adjacent to the (N+1)thfirst symbol 902 is determined to represent erasure. At least one secondsymbol included in the partial second coded data piece 907 providedadjacent to the (N+2)th first symbol 903 is determined not to representerasure.

The number of second symbols which are determined to represent erasureis arbitrary. For example, half of the plurality of second symbolsincluded in each of the second coded data pieces 909 and 910 which areheld between the synchronization data pieces and/or the first coded datapieces may be determined to represent erasure. Alternatively, all such aplurality of second symbols may be determined to represent erasure.

A second symbol determined to represent erasure is associated witherasure locator information representing “1”. A second symbol determinednot to represent erasure is associated with erasure locator informationrepresenting “0”.

In another embodiment, the data pieces 901, 902 and 903 may besynchronization data pieces. In this case also, at least one of theplurality of second symbols arranged immediately on both sides of the(N+1)th synchronization data piece 902 is determined to representerasure. Thus, erasure locator information representing such adetermination result is generated.

For example, at least one second symbol included in the partial secondcoded data piece 904 adjacent to the (N+1)th synchronization data piece902 is determined to represent erasure. At least one second symbolincluded in the partial second coded data piece 906 adjacent to the Nthsynchronization data piece 901 is determined not to represent erasure.

In addition, for example, at least one second symbol included in thepartial second coded data piece 905 adjacent to the (N+1)thsynchronization data piece 902 is determined to represent erasure. Atleast one second symbol included in the partial second coded data piece907 adjacent to the (N+2)th synchronization data piece 903 is determinednot to represent erasure. In this case also, the number of secondsymbols determined to represent erasure is arbitrary.

In still another embodiment, at least one of the data pieces 901, 902and 903 (for example, the data piece 901) may be a synchronization datapiece. The other data pieces are first symbols. In this case also, theerasure locator information is generated in the same procedure as thatdescribed above. (The detailed description of the procedure will not berepeated.)

The above-described method can be applied as follows to the case wherethe errors as shown in FIG. 7 occur. The second symbols located in errorlocation areas 710 and 711 are determined to represent erasure. As aresult of this determination, the partial second coded data pieces 704through 709 each include 12 second symbols determined to representerasure and 5 second symbols determined to represent an error. The totalnumber of the symbols determined to represent erasure and the totalnumber of the symbols determined to represent an error are each in therange of expression 2. Thus, error correction is possible.

In the case where error location information (or synchronizationdetection information) indicates that an error is detected in both ofthe two first symbols adjacent to each other (or two synchronizationdata pieces adjacent to each other), all the second symbols arrangedbetween the two first symbols (or the two synchronization data pieces)are determined to represent erasure.

Next, another method for generating erasure locator information will bedescribed with reference to FIG. 10.

In FIG. 10, mark “X” indicates a synchronization data piece, thesynchronization detection information of which represents “1”, or afirst symbol, the error location information of which represents 1”.Mark “Δ” indicates a synchronization data piece, the synchronizationdetection information of which represents “2” (i.e., a synchronizationdata piece detected with a positional offset).

In one embodiment, an Nth synchronization data piece 1002, an (N+1)thsynchronization data piece 1001, and an (N+2)th synchronization datapiece 1003 are arranged in a recording direction 1006. At least a secondcoded data piece 1004 is provided between the Nth synchronization datapiece 1002 and the (N+1)th synchronization data piece 1001. At least asecond coded data piece 1005 is provided between the (N+1)thsynchronization data piece 1001 and the (N+2)th synchronization datapiece 1003. The second encoded data pieces 1004 and 1005 each include atleast one second symbol. When, as shown in FIG. 10, the (N+1)thsynchronization data piece 1001 is detected with a positional offset, atleast one second symbol provided between the Nth synchronization datapiece 1002 and the (N+1)th synchronization data piece 1001 is determinedto represent erasure. At least one second symbol provided between the(N+1)th synchronization data piece 1001 and the (N+2)th synchronizationdata piece 1003 is determined not to represent erasure. The reason isthat symbols located before the synchronization data piece detected witha positional offset are incorrect with a high probability, and symbolslocated after the synchronization data piece detected with a positionaloffset are correctly reproduced with a high probability.

In another embodiment, the data pieces 1002 and 1003 may be firstsymbols. The first symbol 1002 is provided between the Nthsynchronization data piece and the (N+1)th synchronization data piece1001, and the first symbol 1003 is provided between the (N+1)thsynchronization data piece 1001 and the (N+2)th synchronization datapiece. In this case also, at least one second symbol provided betweenthe first symbol 1002 and the (N+1)th synchronization data piece 1001 isdetermined to represent erasure. At least one second symbol providedbetween the (N+1)th synchronization data piece 1001 and the first symbol1003 is determined not to represent erasure.

The second symbol determined to represent erasure is associated witherasure locator information representing “1”. The second symboldetermined not to represent erasure is associated with erasure locatorinformation representing “0”.

Using this method for generating erasure locator information, a symbollocated before a synchronization data piece and having a highprobability of being incorrect can be determined to represent erasure.Thus, the number of symbols which can be corrected, among incorrectsymbols, is increased. This improves the error correction capability.Also using this method, a symbol located after a synchronization datapiece and having a high probability of being correctly reproduced can bedetermined not to represent erasure. Thus, correct symbols are notdetermined to represent erasure. As a result, the number of unnecessaryerasure positions is reduced, and effective erasure error correction canbe performed. This further improves the error correction capability.

Still another method for generating erasure locator information will bedescribed with reference to FIG. 11.

In FIG. 11, mark “X” indicates a synchronization data piece, thesynchronization detection information of which represents “1” and/or afirst symbol, the error location information of which represents 1”.Mark “◯” indicates a synchronization data piece, the synchronizationdetection information of which represents “0” and/or a first symbol, theerror location information of which represents 0”. Mark “Δ” indicates asynchronization data piece, the synchronization detection information ofwhich represents “2”.

When no synchronization data piece is detected, data pieces which areread before the next time a synchronization data piece is correctlydetected have a high probability of being incorrect. Therefore, when anytwo or more data pieces from the undetected synchronization data piecesand the synchronization data pieces detected with a positional offsetare consecutive, at least one first symbol and at least one secondsymbol provided between the consecutive synchronization data pieces aredetermined to represent erasure.

In one embodiment, synchronization data pieces 1101 and 1102, thesynchronization detection information of which represent “1”, areconsecutive in a recording direction 1118. In this case, even when afirst symbol 1104, the error location information of which represents“0”, exists between the synchronization data pieces 1101 and 1102, it isregarded that information represented by the first symbol 1104accidentally matches a correct code word. Thus, the first symbol 1104 isdetermined to represent erasure. The second symbols included in each ofsecond coded data pieces 1110, 1111, 1112 and 1113 between thesynchronization data pieces 1101 and 1102 are determined to representerasure. The second symbols determined to represent erasure are eachassociated with erasure locator information representing “1”.

In addition in FIG. 11, the synchronization data pieces 1102, thesynchronization detection information of which represent “1”, and asynchronization data piece, the synchronization detection information ofwhich represent “2”, are consecutive in the recording direction 1118. Inthis case, even when a first symbol 1108, the error location informationof which represents “0”, exists between the synchronization data pieces1102 and 1103, it is regarded that information represented by the firstsymbol 1108 accidentally matches a correct code word. Thus, the firstsymbol 1108 is determined to represent erasure. The second symbolsincluded in each of the second coded data pieces 1114, 1115, 1116 and1117 between the synchronization data pieces 1102 and 1103 aredetermined to represent erasure. The second symbols determined torepresent erasure are each associated with erasure locator informationrepresenting “1”. The first symbols 1105, 1106, 1107 and 1109 are firstsymbols determined to be incorrect.

Using this method for generating erasure, a first symbol, which is notdetermined to be incorrect by the conventional methods because itaccidentally represents information matching the correct code worddespite the fact that it is actually incorrect, can now be determined tobe incorrect. Thus, a second symbol can now be correctly determined asrepresenting erasure, while the conventional methods fail in thisbecause the incorrect first symbol is detected as being correct.Therefore, the number of symbols which can be corrected, among incorrectsymbols, is increased. This improves the error correction capability.Since the erasure error correction can be performed with highercertainty, the erasure error correction capability is improved.

FIG. 12 is a flowchart 120 illustrating an exemplary method forcorrecting the erasure error of the second coded data piece 202 asperformed in step 105 in FIG. 1.

In step 1201, a syndrome representing position information forspecifying a position of an error is calculated. A data piece R to beerasure-error-corrected is:R=(B[0]B[1] . . . B[246]B[247])  expression 7

In this expression, B[i] (i=0 through 247) represents 1 byte, whichcorresponds to 8 bits. Here, the data size of one symbol is 1 byte. B[0]through B[215] represent a data portion which show a content (forexample, video) or the like, and B[216] through B[247] represent aparity portion. Syndrome S_(j) is defined as:

=R(+¹)=B[0]α^(247j) +B[1]α^(246j) + . . . +B[246]α^(j)+b[247]  expression 8

Here, j=0 through 31.

In step 1202, it is determined whether syndrome S_(j) is 0 or not. Whensyndrome S_(j) is 0, the processing advances to step 1210. In step 1210,it is determined that all the symbols B[i] (i=0 through 247) included inthe data piece Rare correct, and the erasure error correction isterminated. When syndrome S_(j) is not 0 in step 1202, the processingadvances to step 1203.

In step 1203, an error locator polynomial is formulated using syndromeS_(j) and the erasure locator information. The error locator polynomialhas, as a root, the reciprocal number of error locations L1, L2, . . .Lm (m is the number of errors+the number of erasures) and is representedby expression 5 above.

The coefficient of the error locator polynomial is defined by syndromeS_(j) and the erasure locator information. The coefficient of the errorlocator polynomial is found using Peterson's method, the Euclideanmethod, or an algorithm such as the BM method. Peterson's method solvesthe simultaneous equations realized between the coefficient of the errorlocator polynomial, syndrome S_(j), and the erasure locator information,using a matrix. The Euclidean method is a sequential calculation methodof solving such simultaneous equations using a polynomial.

When the coefficient of the error locator polynomial is found in step1204, the processing advances to step 1205. When the coefficient is notfound, the processing advances to step 1209. In step 1209, it isdetermined that a larger number of errors than can be corrected aregenerated. Thus, it is determined that the correction is impossible andthe erasure error correction procedure is terminated.

In step 1205, α to the -ith power (i=0 through 247, and α which is theroot of the primitive polynomial (expression 1)) is substituted into theerror locator polynomial. Thus, the value of “k”, at which the solutionof the error locator polynomial is 0, is found. In this way, theposition of the incorrect data piece (i.e., the error location) isfound. The symbol corresponding to the error location is represented as:B[247-k]  expression 9.

In step 1206, it is determined whether or not a calculation for findingthe error location can be performed. When it is determined that thecalculation can be performed in step 1206, the processing advances tostep 1207. When it is determined that the calculation cannot beperformed in step 1206, it is determined that correction is impossibleand the erasure error correction procedure is terminated in step 1209.

In step 1207, an error value is calculated by solving the simultaneousequations between the error location found in steps 1205 and 1206,syndrome S_(j) and the erasure locator information.

In step 1208, symbol B[247-k] is erasure-error-corrected by subtractingthe error value obtained in step 1207 from the data value correspondingto the error location found in steps 1205 and 1206. Then, the erasureerror correction is terminated.

As described above, in the first example, when an error is detected in afirst symbol included in a first coded data piece having a high degreeof redundancy or when no synchronization data piece is detected (FIG.9), second symbols provided in the vicinity of such a first symbol orthe undetected synchronization data piece have a high probability ofbeing incorrect and thus are determined to represent erasure. When asynchronization data piece is detected with a positional offset (FIG.10), symbols included in a coded data piece provided before thatsynchronization data piece have a high probability of being incorrectand thus are determined to represent erasure, and symbols included in acoded data piece provided after that synchronization data piece have alow probability of being incorrect and thus are determined not torepresent erasure. When undetected synchronization data pieces and/orsynchronization data pieces detected with a positional offset areconsecutive (FIG. 11), the data pieces, which are read before the nextcorrectly detected synchronization data piece, have a high probabilityof being incorrect. Therefore, symbols included in all the coded datapieces between those consecutive synchronization data pieces aredetermined to represent erasure. Owing to these methods, erasurepositions can be determined with higher precision, and thus the errorcorrection capability can be improved.

Example 2

An error correction method according to a second example of the presentinvention will be described. In the following description, the compositecoded data piece 203 shown in FIG. 2 will be used as an example of thecomposite coded data piece.

FIG. 13 is a flowchart 130 illustrating an error correction method ofthe composite coded data piece 203 in this example. Identical stepspreviously discussed with respect to FIG. 1 bear identical referencenumerals and the detailed descriptions thereof will be omitted.

The flowchart 130 is different from the flowchart 10 in FIG. 1 in thatin flowchart 130, when the second coded data piece is noterror-corrected, erasure error correction is performed repeatedly usingerasure locator information which is generated by a different erasurelocator information generation method. In this example, erasure errorcorrection is performed repeatedly until all the errors are corrected ortermination conditions are fulfilled.

Hereinafter, erasure error correction will be described which uses afirst erasure locator information generation method, a second erasurelocator information generation method, and a third erasure locatorinformation generation method and is terminated when all the first,second and third erasure locator information generation methods are used(termination conditions). These three erasure locator informationgeneration methods are, for example, described with reference to FIGS.9, 10 and 11.

Steps 101, 102 and 103 are performed. Then, in step 1301, the firsterasure locator information generation method is first selected.

In step 1302, the first erasure locator information generation method iscarried out using the synchronization detection information and theerror location information generated in steps 101 and 103. Thus, firsterasure locator information is generated.

In step 105, the second coded data piece is erasure-error-correctedusing the first erasure locator information generated in step 1302. Thepost-correction second coded data piece is referred to as a “firstcorrected data piece”.

In step 1303, it is determined whether all the errors have beencorrected or not. When the second coded data piece includes anuncorrected error in step 1303, the processing advances to step 1304.When all the errors have been corrected in step 1303, the errorcorrection procedure is terminated.

In step 1304, it is determined that the termination conditions are notfulfilled since only one erasure error location information generationmethod has been used. The processing returns to step 1301, where thesecond erasure error location information generation method is selected.The second erasure error location information generation method isdifferent from the first erasure error location information generationmethod already used.

In step 1302, the second erasure locator information generation methodis carried out using the synchronization detection information and theerror location information generated in steps 101 and 103. Thus, seconderasure locator information is generated.

In step 105, the first corrected data piece is erasure-error-correctedusing the second erasure locator information generated in step 1302. Thepost-correction first corrected data piece is referred to as a “secondcorrected data piece”.

In step 1303, it is determined whether all the errors have beencorrected or not. When the first corrected data piece includes anuncorrected error in step 1303, the processing advances to step 1304.When all the errors have been corrected in step 1303, the errorcorrection procedure is terminated.

In step 1304, it is determined that the termination conditions are notfulfilled since only two erasure error location information generationmethods have been used. The processing returns to step 1301, where thethird erasure error location information generation method is selected.The third erasure error location information generation method isdifferent from the first erasure error location information generationmethod and the second erasure error location information generationmethod already used.

In step 1302, the third erasure locator information generation method iscarried out using the synchronization detection information and theerror location information generated in steps 101 and 103. Thus, thirderasure locator information is generated.

In step 105, the second corrected data piece is erasure-error-correctedusing the third erasure locator information generated in step 1302. Thepost-correction second corrected data piece is referred to as a “thirdcorrected data piece”.

In step 1303, it is determined whether all the errors have beencorrected or not. When the second corrected data piece includes anuncorrected error in step 1303, the processing advances to step 1304.When all the errors have been corrected in step 1303, the errorcorrection procedure is terminated.

In step 1304, it is determined that the termination conditions arefulfilled since three erasure error location information generationmethods have been used. Thus, the error correction procedure isterminated.

In the second example, three erasure error location informationgeneration methods are used. The number of erasure error locationinformation generation methods used is arbitrary as long as it is two ormore. Any erasure error location information generation method which cangenerate erasure error location information is usable.

In step 1301 of the second example, the erasure error locationinformation generation methods are selected in the order of first,second and third erasure error location information generation methods.When all the errors are not corrected in step 105, even an erasure errorlocation information generation method which has already been used canbe selected as long as it is not the one which was used immediatelypreviously. When all of the errors can be corrected using a certainerasure error location information generation method, the same erasureerror location information generation method can be selected as thefirst erasure error location information generation method used for adifferent second coded data piece. For example, when all the errors canbe corrected using the first erasure error location information, thefirst erasure error location information generation method can be usedfor erasure error correction of a different second coded data piece.When all the errors can be corrected using the second erasure errorlocation information, the second erasure error location informationgeneration method can be used for erasure error correction of adifferent second coded data piece.

In the second example, the second and third erasure error correction isperformed on the first corrected data piece and the second correcteddata piece. Alternatively, the erasure error correction may be performedon the uncorrected second coded data piece.

In the second example, the procedure is terminated when all three of theerasure error location information generation methods are used. This maybe modified in various ways. For example, any possible combination ofthe three erasure error location information generation methods may beperformed in any possible order, or the three erasure error locationinformation generation methods may be repeated until no correction ismade.

As described above, in the second example, when erasure error correctionis performed using erasure error location information generated by oneerasure error location information generation method but there is atleast one error which cannot be corrected, erasure error correction isperformed in repetition using erasure error location informationgenerated by another erasure error location information generationmethod. Thus, errors which cannot be corrected by performing erasureerror correction once can be corrected. This improves the errorcorrection capability.

Example 3

FIG. 14 shows a structure of an information reproduction apparatus 140according to a third example of the present invention. The informationreproduction apparatus 140 carries out the error correction methodsdescribed in the first and second examples. An exemplary operation ofthe information reproduction apparatus 140 for correcting the compositecoded data piece 203 will be described, mainly using the errorcorrection method shown in FIG. 13. FIGS. 1, 2, 8, 9, 10, 11 and 12 willalso be referred to, but detailed descriptions thereof will not berepeated.

The information reproduction apparatus 140 includes a reproductioncontrol circuit 1402, a rewritable memory 1403, an error correctioncircuit 1408, a microcomputer 1411, and a program memory 1412. Arecording medium 1401 has the composite coded data piece 203 shown inFIG. 2 recorded thereon in the recording direction 202. The compositecoded data piece 203 is merely an example of data which can be recordedon the recording medium 1401.

The reproduction control circuit 1402 includes a reading section 1402Afor reading a composite coded data piece from the recording medium 1401and outputting a first coded data piece, a second coded data piece, anda plurality of synchronization data pieces; and a synchronizationdetection information generation section 1402B for detecting the statesof the plurality of synchronization data pieces and generatingsynchronization detection information representing the detection result.

The rewritable memory 1403 includes a reproduction data area 1404, asynchronization detection information area 1405, an error locationinformation area 1406, and an erasure locator information area 1407. Theerror correction circuit 1408 includes a first error correction circuit1409 and a second error correction circuit 1410. The first errorcorrection circuit 1409 acts as an error location information generationsection for error-correcting the first coded data piece and generatingerror location information representing an error location of the firstcoded data piece. The second error correction circuit 1410 acts as anerasure error correction section for erasure-error-correcting the secondcoded data piece based on the erasure locator information. Themicrocomputer 1411 acts as an erasure locator information generationsection for generating erasure locator information representing anerasure position of the second coded data piece based on the errorlocation information and the synchronization detection information.

As the rewritable memory 1403, a static memory (e.g., SRAM) which doesnot require a data storing operation or a dynamic memory (e.g. DRAM)which requires a data storing operation may be used. In the thirdexample, the area of the rewritable memory 1403 is divided into aplurality of areas which are used as different memory areas.Alternatively, the information reproduction apparatus 140 may include aplurality of rewritable memories 140 for respectively storing differenttypes of data.

The program memory 1412 includes an erasure locator informationgeneration program 1413 and a termination condition branching program1414.

The erasure locator information generation program 1413 causes themicrocomputer 1411 to carry out the erasure locator informationgeneration method described in steps 1301 and 1302 in FIG. 13. Themicrocomputer 1411 generates erasure locator information using thesynchronization detection information and the error location informationwhich are stored in the rewritable memory 1403, and stores the generatederasure locator information in the erasure locator information area1407.

The termination condition branching program 1414 causes themicrocomputer 1411 to carry out the termination condition determinationdescribed in steps 1303 and 1304 in FIG. 13. When it is determined thatthe termination conditions are fulfilled, the microcomputer 1411terminates the error correction procedure. When it is determined thatthe termination conditions are not fulfilled, the microcomputer 1411executes another erasure locator information generation method based onthe erasure locator information generation program 1413.

The reading section 1402A included in the reproduction control circuit1402 reads the composite coded data piece 203 from the recording medium1401. When the reproduced first and second coded data pieces have beeninterleaved, the reading section 1402A de-interleaves these data pieces.The reproduced first and second coded data pieces 201 and 202 are storedin the reproduction data area 1404. The reproduction data area 1404 maybe divided into an area for storing the first coded data piece 201 andan area for storing the second coded data piece 202. The synchronizationdetection information generation section 1402B included in thereproduction control circuit 1402 detects a plurality of synchronizationdata pieces including the synchronization data pieces 204 and 205. Thesynchronization detection information generation section 1402B thenexecutes, for example, the synchronization detection informationgeneration method described in step 101 in FIG. 1 so as to generatesynchronization detection information 1402C. The synchronizationdetection information generation section 1402B stores the generatedsynchronization detection information 1402C in the synchronizationdetection information area 1405.

The first error correction circuit 1409 performs error correction on thefirst coded data piece 201 which is stored in the reproduction data area1404. The first error correction circuit 1409 then executes, forexample, the error location information generation method described insteps 811 through 813 in FIG. 8 so as to generate error locationinformation 1409A. The first error correction circuit 1409 stores thegenerated error location information 1409A in the error locationinformation area 1406. Any circuit may be used as the first errorcorrection circuit 1409 as long as it can perform the processing shownin FIG. 8 on the first coded data piece 201 stored in the reproductiondata area 1404 and store the generated error location information 1409Ain the error location information area 1406.

The microcomputer 1411 analyzes and executes the erasure locatorinformation generation program 1413 stored in the program memory 1412 soas to generate erasure locator information 1411A, and stores thegenerated erasure locator information 1411A in the erasure locatorinformation area 1407. When being notified by the second errorcorrection circuit 1410 that the error is not correctable, themicrocomputer 1411 analyzes and executes the termination conditionbranching program 1414. When the termination conditions are determinedto be fulfilled, the microcomputer 1411 terminates the error correctionprocedure. When the termination conditions are determined not to befulfilled, the microcomputer 1411 analyzes and executes another erasurelocator information generation method contained in the erasure locatorinformation generation program 1413. Thus, the microcomputer 1411generates another erasure locator information 1411B used for repeatingerasure error correction and stores the erasure locator information1411B in the erasure locator information area 1407.

The second error correction circuit 1410 performs erasure errorcorrection of the second coded data piece 202 which is stored in thereproduction data area 1404 using the erasure locator information 1411Aor the erasure locator information 1411B stored in the erasure locatorinformation area 1407. The second error correction circuit 1410 notifiesthe error correction result to the microcomputer 1411. Any circuit maybe used as the second error correction circuit 1410 as long as it canperform the processing shown in FIG. 12 on the second coded data piece202 stored in the reproduction data area 1404 and notify themicrocomputer 1411 whether error correction has been performed (step1208 in FIG. 12), error correction is impossible (step 1209) or there isno error (step 1210).

In the third example, the information reproduction apparatus 140reproduces the first coded data piece 201 and the second coded datapiece 202 using an error correction method. The structures of the firstcoded data piece 201 and the second coded data piece 202 shown in FIG. 2are merely exemplary. Any codes may be used as the first errorcorrection code and the second error correction code as long as thefirst error correction code has a higher degree of redundancy than thatof the second error correction code.

Apart of the procedure performed by the reproduction control circuit1402 and the error correction circuit 1408 may be executed usingsoftware. The procedure performed by the erasure locator informationgeneration program 1413 and the termination condition branching program1414 may be executed by hardware instead of using the programs 1413 and1414.

If all the procedures performed by the information reproductionapparatus 140 are executed by hardware, one device of hardware isrequired for each of the plurality of erasure locator informationgeneration methods. This excessively enlarges the scale of theapparatus. If all the procedures performed by the informationreproduction apparatus 140 are executed by software, an excessively longtime is required. In the third example, the procedure of generatingerasure locator information is performed by software, and otherprocedures are performed by hardware. Thus, erasure error correction canbe performed in repetition merely by reading different programs from theprogram memory 1412. This can reduce the scale of the hardware andshortens the processing time. The information reproduction apparatus 140is superior in terms of the time required for designing and costs tosystems of either executing all the procedures by hardware or executingall the procedures by software.

An error correction method and a reproduction apparatus according to thepresent invention function as follows. When a first symbol included in afirst coded data piece having a relatively high degree of redundancy isdetected to have an error or when no synchronization data piece isdetected, the second symbols which are provided in the vicinity of sucha first symbol or the undetected synchronization data piece have a highprobability of incorrect and thus are determined to represent erasure.When a synchronization data piece is detected with a positional offset,symbols included in the coded data pieces located before such asynchronization data piece have a high probability of being incorrectand thus is determined to represent erasure. Symbols included in thecoded data pieces located after such a synchronization data piece have ahigh probability of being correct and thus is determined not torepresent erasure. When at least two of the undetected synchronizationdata pieces and synchronization data pieces detected with a positionaloffset are consecutive, data pieces which are read before the nextcorrectly detected synchronization data piece have a high probability ofbeing incorrect. Thus, symbols included in all the coded data piecesbetween those consecutive synchronization data pieces are determined torepresent erasure. Owing to these methods, erasure positions can bedetermined with higher precision, and thus the error correctioncapability can be improved.

An error correction method and a reproduction apparatus according to thepresent invention are useful for, for example, error correction ofcomposite coded data.

Various other modifications will be apparent to and can be readily madeby those skilled in the art without departing from the scope and spiritof this invention. Accordingly, it is not intended that the scope of theclaims appended hereto be limited to the description as set forthherein, but rather that the claims be broadly construed.

1. A reproduction method for reproducing a coded data piece from arecording medium having a plurality of synchronization data pieces andthe coded data piece which is error-correction-coded recorded thereon,wherein: the coded data piece includes a plurality of symbols, at leastone of the plurality of symbols is provided between two adjacentsynchronization data pieces among the plurality of synchronization datapieces, and the plurality of synchronization data pieces include an Nthsynchronization data piece, an (N+1)th synchronization data piece, andan (N+2)th synchronization data piece, where N is an integer, thereproduction method comprising: a reading step of reading the pluralityof synchronization data pieces and the coded data piece from therecording medium; a synchronization detection information generationstep of detecting states of the plurality of synchronization data piecesand generating synchronization detection information which representsthe detection result; an erasure locator information generation step ofgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction step of performing erasureerror correction of the coded data piece based on the erasure locatorinformation, wherein the erasure locator information generation stepincludes the step of, when the synchronization detection informationindicates that the Nth synchronization data piece and the (N+2)thsynchronization data piece are detected and the (N+1)th synchronizationdata piece is not detected, determining at least one of the plurality ofsymbols provided adjacent to the (N+1)th synchronization data piece asrepresenting erasure.
 2. A reproduction method according to claim 1,wherein the erasure locator information generation step further includesthe step of, when the synchronization detection information indicatesthat the Nth synchronization data piece and the (N+2)th synchronizationdata piece are detected and the (N+1)th synchronization data piece isnot detected, determining at least one symbol provided adjacent to the(N+1)th synchronization data piece, among at least one symbol providedbetween the Nth synchronization data piece and the (N+1)thsynchronization data piece as representing erasure; and determining atleast one symbol provided adjacent to the (N+1)th synchronization datapiece, among at least one symbol provided between the (N+1)thsynchronization data piece and the (N+2)th synchronization data piece asrepresenting erasure.
 3. A reproduction method according to claim 1,wherein the erasure locator information generation step further includesthe step of, when the synchronization detection information indicatesthat neither of the two adjacent synchronization data pieces aredetected, determining all the symbols provided between the twoundetected synchronization data pieces as representing erasure.
 4. Areproduction method for reproducing a coded data piece from a recordingmedium having a plurality of synchronization data pieces and the codeddata piece which is error-correction-coded recorded thereon, wherein:the coded data piece includes a plurality of symbols, and at least twoof the plurality of symbols are provided between two adjacentsynchronization data pieces of the plurality of synchronization datapieces, the reproduction method comprising: a reading step of readingthe plurality of synchronization data pieces and the coded data piecefrom the recording medium; a synchronization detection informationgeneration step of detecting states of the plurality of synchronizationdata pieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration step of generating erasure locator information whichrepresents an erasure position of the coded data piece, based on thesynchronization detection information; and an erasure error correctionstep of performing erasure error correction of the coded data piecebased on the erasure locator information, wherein the erasure locatorinformation generation step includes the step of, when thesynchronization detection information indicates that a synchronizationdata piece adjacent to a detected synchronization data piece is notdetected, determining at least one symbol adjacent to the undetectedsynchronization data piece, among at least two symbols provided betweenthe detected synchronization data piece and the undetectedsynchronization data piece, as representing erasure; and determining atleast one symbol provided adjacent to the detected synchronization datapiece as not representing erasure.
 5. A reproduction method according toclaim 4, wherein the erasure locator information generation step furtherincludes the step of, when the synchronization detection informationindicates that neither of the two adjacent synchronization data piecesare detected, determining all the symbols provided between the twoundetected synchronization data pieces as representing erasure.
 6. Areproduction method for reproducing a coded data piece from a recordingmedium having a plurality of synchronization data pieces and the codeddata piece which is error-correction-coded recorded thereon, wherein:the coded data piece includes a plurality of symbols, at least one ofthe plurality of symbols is provided between two adjacentsynchronization data pieces among the plurality of synchronization datapieces, and the plurality of synchronization data pieces include an Nthsynchronization data piece and an (N+1)th synchronization data piece,where N is an integer, the reproduction method comprising: a readingstep of reading the plurality of synchronization data pieces and thecoded data piece from the recording medium; a synchronization detectioninformation generation step of detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an erasure locatorinformation generation step of generating erasure locator informationwhich represents an erasure position of the coded data piece, based onthe synchronization detection information; and an erasure errorcorrection step of performing erasure error correction of the coded datapiece based on the erasure locator information, wherein the erasurelocator information generation step includes the step of, when thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one symbol provided between the Nth synchronizationdata piece and the (N+1)th synchronization data piece as representingerasure.
 7. A reproduction method according to claim 6, wherein: theplurality of synchronization data pieces include an (N+2)thsynchronization data piece, and the erasure locator informationgeneration step further includes the step of, when the synchronizationdetection information indicates that the (N+1)th synchronization datapiece is detected with a positional offset, determining at least onesymbol provided between the (N+1)th synchronization data piece and the(N+2)th synchronization data piece as not representing erasure.
 8. Areproduction method for reproducing a coded data piece from a recordingmedium having a plurality of synchronization data pieces and the codeddata piece which is error-correction-coded recorded thereon, wherein:the coded data piece includes a plurality of symbols, and at least oneof the plurality of symbols is provided between two adjacentsynchronization data pieces of the plurality of synchronization datapieces, the reproduction method comprising: a reading step of readingthe plurality of synchronization data pieces and the coded data piecefrom the recording medium; a synchronization detection informationgeneration step of detecting states of the plurality of synchronizationdata pieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration step of generating erasure locator information whichrepresents an erasure position of the coded data piece, based on thesynchronization detection information; and an erasure error correctionstep of performing erasure error correction of the coded data piecebased on the erasure locator information, wherein the erasure locatorinformation generation step includes the step of, when thesynchronization detection information indicates that any two or moredata pieces from undetected synchronization data pieces andsynchronization data pieces detected with a positional offset areconsecutive, determining at least one symbol provided between theconsecutive synchronization data pieces as representing erasure.
 9. Areproduction method for reproducing a coded data piece from a recordingmedium having a plurality of synchronization data pieces and the codeddata piece which is error-correction-coded recorded thereon, wherein:the coded data piece includes a plurality of symbols, and at least oneof the plurality of symbols is provided between two adjacentsynchronization data pieces among the plurality of synchronization datapieces, the reproduction method comprising: a reading step of readingthe plurality of synchronization data pieces and the coded data piecefrom the recording medium; a synchronization detection informationgeneration step of detecting states of the plurality of synchronizationdata pieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration step of generating at least first erasure locator informationand second erasure locator information which represent an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction step of performing erasureerror correction of the coded data piece based on at least one of thefirst erasure locator information and the second erasure locatorinformation, wherein the erasure error correction step includes the stepof, when there is an error which cannot be corrected based on the firsterasure locator information, performing erasure error correction of thecoded data piece based on the second erasure locator information.
 10. Areproduction method according to claim 9, wherein: the erasure locatorinformation generation step includes the steps of: when all the errorscan be corrected based on the first erasure locator information,generating erasure locator information for erasure error correction ofanother coded data piece using an identical method as the method usedfor generating the first erasure locator information, and when all theerrors can be corrected based on the second erasure locator information,generating erasure locator information for erasure error correction ofanother coded data piece using an identical method as the method usedfor generating the second erasure locator information.
 11. Areproduction method according to claim 9, wherein: the plurality ofsynchronization data pieces include an Nth synchronization data piece,an (N+1)th synchronization data piece, and an (N+2)th synchronizationdata piece, where N is an integer, and the erasure locator informationgeneration step includes the step of, when the synchronization detectioninformation indicates that the Nth synchronization data piece and the(N+2)th synchronization data piece are detected and the (N+1)thsynchronization data piece is not detected, determining at least one ofthe plurality of symbols provided adjacent to the (N+1)thsynchronization data piece as representing erasure.
 12. A reproductionmethod according to claim 9, wherein: the plurality of synchronizationdata pieces include an Nth synchronization data piece and an (N+1)thsynchronization data piece, where N is an integer, and the erasurelocator information generation step includes the step of, when thesynchronization detection information indicates that the (N+1)thsynchronization data piece is detected with a positional offset,determining at least one symbol provided between the Nth synchronizationdata piece and the (N+1)th synchronization data piece as representingerasure.
 13. A reproduction method according to claim 9, wherein theerasure locator information generation step includes the step of, whenthe synchronization detection information indicates that any two or moredata pieces from undetected synchronization data pieces andsynchronization data pieces detected with a positional offset areconsecutive, determining at least one symbol provided between theconsecutive synchronization data pieces as representing erasure.
 14. Areproduction apparatus for reproducing a coded data piece from arecording medium having a plurality of synchronization data pieces andthe coded data piece which is error-correction-coded recorded thereon,wherein: the coded data piece includes a plurality of symbols, at leastone of the plurality of symbols is provided between two adjacentsynchronization data pieces among the plurality of synchronization datapieces, and the plurality of synchronization data pieces include an Nthsynchronization data piece, an (N+1)th synchronization data piece, andan (N+2)th synchronization data piece, where N is an integer, thereproduction apparatus comprising: a reading section for reading theplurality of synchronization data pieces and the coded data piece fromthe recording medium; a synchronization detection information generationsection for detecting states of the plurality of synchronization datapieces and generating synchronization detection information whichrepresents the detection result; an erasure locator informationgeneration section for generating erasure locator information whichrepresents an erasure position of the coded data piece, based on thesynchronization detection information; and an erasure error correctionsection for performing erasure error correction of the coded data piecebased on the erasure locator information, wherein when thesynchronization detection information indicates that the Nthsynchronization data piece and the (N+2)th synchronization data pieceare detected and the (N+1)th synchronization data piece is not detected,the erasure locator information generation section determines at leastone of the plurality of symbols provided adjacent to the (N+1)thsynchronization data piece as representing erasure.
 15. A reproductionapparatus according to claim 14, wherein when the synchronizationdetection information indicates that the Nth synchronization data pieceand the (N+2)th synchronization data piece are detected and the (N+1)thsynchronization data piece is not detected, the erasure locatorinformation generation section determines at least one symbol providedadjacent to the (N+1)th synchronization data piece, among at least onesymbol provided between the Nth synchronization data piece and the(N+1)th synchronization data piece as representing erasure; anddetermines at least one symbol provided adjacent to the (N+1)thsynchronization data piece, among at least one symbol provided betweenthe (N+1)th synchronization data piece and the (N+2)th synchronizationdata piece as representing erasure.
 16. A reproduction apparatusaccording to claim 14, wherein when the synchronization detectioninformation indicates that neither of the two adjacent synchronizationdata pieces are detected, the erasure locator information generationsection determines all the symbols provided between the two undetectedsynchronization data pieces as representing erasure.
 17. A reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon, wherein: thecoded data piece includes a plurality of symbols, and at least two ofthe plurality of symbols are provided between two adjacentsynchronization data pieces of the plurality of synchronization datapieces, the reproduction apparatus comprising: a reading section forreading the plurality of synchronization data pieces and the coded datapiece from the recording medium; a synchronization detection informationgeneration section for detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an erasure locatorinformation generation section for generating erasure locatorinformation which represents an erasure position of the coded datapiece, based on the synchronization detection information; and anerasure error correction section for performing erasure error correctionof the coded data piece based on the erasure locator information,wherein when the synchronization detection information indicates that asynchronization data piece adjacent to a detected synchronization datapiece is not detected, the erasure locator information generationsection determines at least one symbol provided adjacent to theundetected synchronization data piece, among at least two symbolsprovided between the detected synchronization data piece and theundetected synchronization data piece, as representing erasure; anddetermines at least one symbol provided adjacent to the detectedsynchronization data piece as not representing erasure.
 18. Areproduction apparatus according to claim 17, wherein when thesynchronization detection information indicates that neither of the twoadjacent synchronization data pieces are detected, the erasure locatorinformation generation section determines all the symbols providedbetween the two undetected synchronization data pieces as representingerasure.
 19. A reproduction apparatus for reproducing a coded data piecefrom a recording medium having a plurality of synchronization datapieces and the coded data piece which is error-correction-coded recordedthereon, wherein: the coded data piece includes a plurality of symbols,at least one of the plurality of symbols is provided between twoadjacent synchronization data pieces among the plurality ofsynchronization data pieces, and the plurality of synchronization datapieces include an Nth synchronization data piece and an (N+1)thsynchronization data piece, where N is an integer, the reproductionapparatus comprising: a reading section for reading the plurality ofsynchronization data pieces and the coded data piece from the recordingmedium; a synchronization detection information generation section fordetecting states of the plurality of synchronization data pieces andgenerating synchronization detection information which represents thedetection result; an erasure locator information generation section forgenerating erasure locator information which represents an erasureposition of the coded data piece, based on the synchronization detectioninformation; and an erasure error correction section for performingerasure error correction of the coded data piece based on the erasurelocator information, wherein when the synchronization detectioninformation indicates that the (N+1)th synchronization data piece isdetected with a positional offset, the erasure locator informationgeneration section determines at least one symbol provided between theNth synchronization data piece and the (N+1)th synchronization datapiece as representing erasure.
 20. A reproduction apparatus according toclaim 19, wherein: the plurality of synchronization data pieces includean (N+2)th synchronization data piece, and when the synchronizationdetection information indicates that the (N+1)th synchronization datapiece is detected with a positional offset, the erasure locatorinformation generation section determines at least one symbol providedbetween the (N+1)th synchronization data piece and the (N+2)thsynchronization data piece as not representing erasure.
 21. Areproduction apparatus for reproducing a coded data piece from arecording medium having a plurality of synchronization data pieces andthe coded data piece which is error-correction-coded recorded thereon,wherein: the coded data piece includes a plurality of symbols, and atleast one of the plurality of symbols is provided between two adjacentsynchronization data pieces of the plurality of synchronization datapieces, the reproduction apparatus comprising: a reading section forreading the plurality of synchronization data pieces and the coded datapiece from the recording medium; a synchronization detection informationgeneration section for detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an erasure locatorinformation generation section for generating erasure locatorinformation which represents an erasure position of the coded datapiece, based on the synchronization detection information; and anerasure error correction section for performing erasure error correctionof the coded data piece based on the erasure locator information,wherein when the synchronization detection information indicates thatany two or more data pieces from undetected synchronization data piecesand synchronization data pieces detected with a positional offset areconsecutive, the erasure locator information generation sectiondetermines at least one symbol provided between the consecutivesynchronization data pieces as representing erasure.
 22. A reproductionapparatus for reproducing a coded data piece from a recording mediumhaving a plurality of synchronization data pieces and the coded datapiece which is error-correction-coded recorded thereon, wherein: thecoded data piece includes a plurality of symbols, and at least one ofthe plurality of symbols is provided between two adjacentsynchronization data pieces among the plurality of synchronization datapieces, the reproduction apparatus comprising: a reading section forreading the plurality of synchronization data pieces and the coded datapiece from the recording medium; a synchronization detection informationgeneration section for detecting states of the plurality ofsynchronization data pieces and generating synchronization detectioninformation which represents the detection result; an erasure locatorinformation generation section for generating at least first erasurelocator information and second erasure locator information whichrepresent an erasure position of the coded data piece, based on thesynchronization detection information; and an erasure error correctionsection for performing erasure error correction of the coded data piecebased on at least one of the first erasure locator information and thesecond erasure locator information, wherein when there is an error whichcannot be corrected based on the first erasure locator information, theerasure error correction section performs erasure error correction ofthe coded data piece based on the second erasure locator information.23. A reproduction apparatus according to claim 22, wherein: when allthe errors can be corrected based on the first erasure locatorinformation, the erasure locator information generation sectiongenerates erasure locator information for erasure error correction ofanother coded data piece using an identical method as the method usedfor generating the first erasure locator information, and when all theerrors can be corrected based on the second erasure locator information,the erasure locator information generation section generates erasurelocator information for erasure error correction of another coded datapiece using an identical method as the method used for generating thesecond erasure locator information.
 24. A reproduction apparatusaccording to claim 22, wherein: the plurality of synchronization datapieces include an Nth synchronization data piece, an (N+1)thsynchronization data piece, and an (N+2)th synchronization data piece,where N is an integer, and when the synchronization detectioninformation indicates that the Nth synchronization data piece and the(N+2)th synchronization data piece are detected and the (N+1)thsynchronization data piece is not detected, the erasure locatorinformation generation section determines at least one of the pluralityof symbols provided adjacent to the (N+1)th synchronization data pieceas representing erasure.
 25. A reproduction apparatus according to claim22, wherein: the plurality of synchronization data pieces include an Nthsynchronization data piece and an (N+1)th synchronization data piece,where N is an integer, and when the synchronization detectioninformation indicates that the (N+1)th synchronization data piece isdetected with a positional offset, the erasure locator informationgeneration section determines at least one symbol provided between theNth synchronization data piece and the (N+1)th synchronization datapiece as representing erasure.
 26. A reproduction apparatus according toclaim 22, wherein: when the synchronization detection informationindicates that any two or more data pieces from undetectedsynchronization data pieces and synchronization data pieces detectedwith a positional offset are consecutive, the erasure locatorinformation generation section determines at least one symbol providedbetween the consecutive synchronization data pieces as representingerasure.